Determine whether each statement is true or false . If false , replace the underlined word or number to make a true statement.

1. The exponent of a number raised to the first power can be omitted.

SOLUTION:  An exponent tells how many times a number is used as a factor. So, the exponent of a number raised to the first power can be omitted. The statement is true.

2. A number is in scientific notation when it does not contain exponents.

SOLUTION:  A number that is expressed as a product of a factor and a power of 10 is written in scientific notation. So, the statement is false. A number is in standard form when it does not contain exponents.

3. In 57, the number 7 is the base.

SOLUTION:  

The number that is multiplied is called the base. So, the statement is false. In 57, the number 7 is the exponent.

4. The number 49 is an example of a(n) prime number.

SOLUTION:  A prime number is a whole number that has exactly two unique factors, 1 and itself. So, the statement is false. The number 49 is an example of a composite number.

5. The equation y = 5x + 2 is an example of a(n) exponential function.

SOLUTION:  

An exponential function is a function that can be described by an equation of the form y = ax + c, where a ≠ 0 and 

a ≠ 1. So, the statement is true.

6. The graph of a(n) cubic function is called a parabola.

SOLUTION:  The statement is false. The graph of a quadratic function is called a parabola.

7. To multiply powers with the same base, add the exponents.

SOLUTION:  The statement is true.

8. A(n) nonlinear function has a constant rate of change.

SOLUTION:  Nonlinear functions do not have constant rates of change. So, the statement is false. A linear function has a constant rate of change.

9. To simplify (n6)5, the first step is to add 6 and 5.

SOLUTION:  

To find the power of a power, multiply exponents. So, the statement is false. To simplify (n6)5, the first step is to

multiply 6 and 5.

10. The graph of a(n) quadratic function is symmetric.

SOLUTION:  The graph of a quadratic function is a parabola, which is symmetric. So, the statement is true.

Write each expression using exponents.11. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

12. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

13. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

14. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

15. 35

SOLUTION:  

16. 2 • 43

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

17. x2 – 6

SOLUTION:  

18. w3 + y2

SOLUTION:  

19. 2(y + z3)

SOLUTION:  

20. w4x

2yz

SOLUTION:  

21. TEETH Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

Write the prime factorization of each number. Use exponents for repeated factors.22. 34

SOLUTION:  34 = 2 • 17

23. 40

SOLUTION:  

24. 63

SOLUTION:  

25. 225

SOLUTION:  

Factor each monomial.26. 18x

SOLUTION:  18x = 2 • 3 • 3 • x

27. 10r2

SOLUTION:  

28. 32pq

SOLUTION:  32pq = 2 • 2 • 2 • 2 • 2 • p • q

29. –25ab2

SOLUTION:  

30. PHOTOGRAPHS Jacy has 24 photographs to put in a rectangular arrangement. In how many different numbers of rows and columns can she display them if each row has the same number of photographs? Name each arrangement.

SOLUTION:  List the different numbers of rows and columns by listing the factors of 24. So, Jacy could form rectangles with the following number of rows and columns: 1 • 24, 24 • 1, 2 • 12, 12 • 2, 3 • 8, 8 • 3, 4 • 6, 6 • 4. There are 8 different arrangements.

Find each product or quotient. Express using exponents.

31. 35 • 3

2

SOLUTION:  

32. (–7) • (–7)4

SOLUTION:  

33. m3 • m6

SOLUTION:  

34. x8 • x

SOLUTION:  

35. (2h7)(6h)

SOLUTION:  

36. (5a3)(–6a

4)

SOLUTION:  

37. 

SOLUTION:  

38. 

SOLUTION:  

39. PLANETS Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how

many times farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by thedistance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Write each expression using a positive exponent.

40. 9–4

SOLUTION:  

9–4

=

41. (–10)–2

SOLUTION:  

(–10)–2

=

42. m–5

SOLUTION:  

m–5 =

Write each fraction as an expression using a negative exponent other than –1.

43. 

SOLUTION:  

= 6–3

44. 

SOLUTION:  

or  or 

45. 

SOLUTION:  

46. MEASUREMENT If 1 millimeter is equal to 10–3

meter and 1 nanometer is equal to 10–9

meter, how many nanometers are in 1 millimeter? Write using a positive exponent.

SOLUTION:  To find the number of nanometers in 1 millimeter, divide the number of millimeters in a meter by the number of nanometers in a meter.

So, there are 106 nanometers in 1 millimeter.

Express each number in standard form.

47. 5.82 × 103

SOLUTION:  

48. 9.0 × 10–2

SOLUTION:  

49. 3.4 × 10–4

SOLUTION:  

50. 1.705 × 105

SOLUTION:  

Express each number in scientific notation.51. 379

SOLUTION:  

52. 26,880

SOLUTION:  

53. 0.0014

SOLUTION:  

54. 0.000561

SOLUTION:  

55. SPACE The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Simplify.

56. (26)3

SOLUTION:  

57. (r2)8

SOLUTION:  

58. (3x7)2

SOLUTION:  

59. (–2n4)6

SOLUTION:  

60. (4a9b)

4

SOLUTION:  

61. (5w5x

8)3

SOLUTION:  

62. GEOMETRY Find the area of the square shown below.

SOLUTION:  

Determine whether each graph, equation, or table represents a linear or nonlinear function. Explain.

63. 

SOLUTION:  The graph is a curve, not a straight line. So, it represents a nonlinear function.

64. 

SOLUTION:  The graph is a line. So, it represents a linear function.

65. y = x

SOLUTION:  

The equation y = x represents a linear function, because it is written in the form y = mx + b.

66. y =  + 1

SOLUTION:  

The equation y =  + 1 represents a nonlinear function, because it cannot be written in the form y = mx + b.

67. 

SOLUTION:  As x increases by 1, y decreases by 2. So, this is a linear function.

68. 

SOLUTION:  As x increases by 1, y increases by 10. So, this is a linear function.

69. SCHOOLS A school district’s spending on students over the last five years is represented by the equation y =

325x2 + 0.2x + 1427. Is this equation linear? Explain.

SOLUTION:  

The equation y = 325x2 + 0.2x + 1427 represents a nonlinear function, because it cannot be written in the form y =

mx + b.

Graph each function.

70. y = 3x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x2 (x, y)

–2 y = 3(–2)2 = 12 (–2, 12)

–1 y = 3(–1)2 = 3 (–1, 3)

0 y = 3(0)2 = 0 (0, 0)

1 y = 3(1)2 = 3 (1, 3)

2 y = 3(2)2 = 12 (2, 12)

71. y = –2x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –2x2 (x, y)

–2 y = –2(–2)2 = –8 (–2, –8)

–1 y = –2(–1)2 = –2 (–1, –2)

0 y = –2(0)2 = 0 (0, 0)

1 y = –2(1)2 = –2 (1, –2)

2 y = –2(2)2 = –8 (2, –8)

72. y = x2 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x2 – 4 (x, y)

–2 y = (–2)2 – 4 = 0 (–2, 0)

–1 y = (–1)2 – 4 = –3 (–1, –3)

0 y = 02 – 4 = –4 (0, –4)

1 y = 12 – 4 = –3 (1, –3)

2 y = 22 – 4 = 0 (2, 0)

73. y = –x2 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –x2 + 1 (x, y)

–2 y = –(–2)2 + 1 = –3 (–2, –3)

–1 y = –(–1)2 + 1 = 0 (–1, 0)

0 y = –(0)2 + 1 = 1 (0, 1)

1 y = –(1)2 + 1 = 0 (1, 0)

2 y = –(2)2 + 1 = –3 (2, –3)

74. y = 2x2 + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x2 + 2 (x, y)

–2 y = 2(–2)2 + 2 = 10 (–2, 10)

–1 y = 2(–1)2 + 2 = 4 (–1, 4)

0 y = 2(0)2 + 2 = 2 (0, 2)

1 y = 2(1)2 + 2 = 4 (1, 4)

2 y = 2(2)2 + 2 = 10 (2, 10)

75. y = x2 – 3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x

2 – 3

(x, y)

–2 y = (–2)

2 – 3 = –1

(–2, –1)

–1 y = (–1)

2 – 3 = –2.5

(–1, –2.5)

0 y = (0)

2 – 3 = –3

(0, –3)

1 y = (1)

2 – 3 = –2.5

(1, –2.5)

2 y = (2)

2 – 3 = –1

(2, –1)

76. GEOMETRY The volume of a cylinder with a height of 8 inches can be found using the equation V = 8(3.14)r2

where r is the radius of the cylinder. Graph the equation.

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

r V = 8(3.14)r2 (r, V)

0 V = 8(3.14)(02) = 0 (0, 0)

1 V = 8(3.14)(12) = 25.12 (1, 25.12)

2 V = 8(3.14)(22) = 100.48 (2, 100.48)

3 V = 8(3.14)(32) = 226.08 (3, 226.08)

4 V = 8(3.14)(42) = 401.92 (4, 401.92)

Graph each function.

77. y = x3 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 + 1 (x, y)

–2 y = (–2)3 + 1 = –7 (–2, –7)

–1 y = (–1)3 + 1 = 0 (–1, 0)

0 y = 03 + 1 = 1 (0, 1)

1 y = 13 + 1 = 2 (1, 2)

2 y = 23 + 1 = 9 (2, 9)

78. y = –3x3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –3x3 (x, y)

–2 y = –3(–2)3 = 24 (–2, 24)

–1 y = –3(–1)3 = 3 (–1, 3)

0 y = –3(0)3 = 0 (0, 0)

1 y = –3(1)3 = –3 (1, –3)

2 y = –3(2)3 = –24 (2, –24)

79. y = x3 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 – 4 (x, y)

–2 y = (–2)3 – 4 = –12 (–2, –12)

–1 y = (–1)3 – 4 = –5 (–1, –5)

0 y = 03 – 4 = –4 (0, –4)

1 y = 13 – 4 = –3 (1, –3)

2 y = 23 – 4 = 4 (2, 4)

80. y = 2x + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x + 2 (x, y)

–2 y = 2–2

+ 2 = 2.25 (–2, 2.25)

–1 y = 2–1

+ 2 = 2.5 (–1, 2.5)

0 y = 20+ 2 = 3 (0, 3)

1 y = 21 + 2 = 4 (1, 4)

2 y = 22 + 2 = 6 (2, 6)

81. y = 3x

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x (x, y)

–2 y = 3

–2 =

(–2, )

–1 y = 3

–1 =

(–1, )

0 y = 30 = 1 (0, 1)

1 y = 31 = 3 (1, 3)

2 y = 32 = 9 (2, 9)

82. y = 2x – 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x – 1 (x, y)

–2 y = 2–2

– 1 = –0.75 (–2, –0.75)

–1 y = 2–1

– 1 = –0.5 (–1, –0.5)

0 y = 20 – 1 = 0 (0, 0)

1 y = 21 – 1 = 1 (1, 1)

2 y = 22 – 1 = 3 (2, 3)

83. LIFE SCIENCE Starting from a single bacterium in a dish, the number of bacteria after t cycles of reproduction is

2t. A bacterium reproduces every 30 minutes. If there are 1000 bacteria in a dish now, how many will there be in 1

hour?

SOLUTION:  

To find the number of bacteria will be in the dish in 1 hour, replace t with 2 in the expression 2t because there are 2

thirty minute cycles in 2 hour. Then, multiply the result by 1000 because there are 1000 bacteria in the dish now.

So, there will be 4000 bacteria in the dish in 1 hour.

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Study Guide and Review

Determine whether each statement is true or false . If false , replace the underlined word or number to make a true statement.

1. The exponent of a number raised to the first power can be omitted.

SOLUTION:  An exponent tells how many times a number is used as a factor. So, the exponent of a number raised to the first power can be omitted. The statement is true.

2. A number is in scientific notation when it does not contain exponents.

SOLUTION:  A number that is expressed as a product of a factor and a power of 10 is written in scientific notation. So, the statement is false. A number is in standard form when it does not contain exponents.

3. In 57, the number 7 is the base.

SOLUTION:  

The number that is multiplied is called the base. So, the statement is false. In 57, the number 7 is the exponent.

4. The number 49 is an example of a(n) prime number.

SOLUTION:  A prime number is a whole number that has exactly two unique factors, 1 and itself. So, the statement is false. The number 49 is an example of a composite number.

5. The equation y = 5x + 2 is an example of a(n) exponential function.

SOLUTION:  

An exponential function is a function that can be described by an equation of the form y = ax + c, where a ≠ 0 and 

a ≠ 1. So, the statement is true.

6. The graph of a(n) cubic function is called a parabola.

SOLUTION:  The statement is false. The graph of a quadratic function is called a parabola.

7. To multiply powers with the same base, add the exponents.

SOLUTION:  The statement is true.

8. A(n) nonlinear function has a constant rate of change.

SOLUTION:  Nonlinear functions do not have constant rates of change. So, the statement is false. A linear function has a constant rate of change.

9. To simplify (n6)5, the first step is to add 6 and 5.

SOLUTION:  

To find the power of a power, multiply exponents. So, the statement is false. To simplify (n6)5, the first step is to

multiply 6 and 5.

10. The graph of a(n) quadratic function is symmetric.

SOLUTION:  The graph of a quadratic function is a parabola, which is symmetric. So, the statement is true.

Write each expression using exponents.11. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

12. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

13. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

14. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

15. 35

SOLUTION:  

16. 2 • 43

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

17. x2 – 6

SOLUTION:  

18. w3 + y2

SOLUTION:  

19. 2(y + z3)

SOLUTION:  

20. w4x

2yz

SOLUTION:  

21. TEETH Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

Write the prime factorization of each number. Use exponents for repeated factors.22. 34

SOLUTION:  34 = 2 • 17

23. 40

SOLUTION:  

24. 63

SOLUTION:  

25. 225

SOLUTION:  

Factor each monomial.26. 18x

SOLUTION:  18x = 2 • 3 • 3 • x

27. 10r2

SOLUTION:  

28. 32pq

SOLUTION:  32pq = 2 • 2 • 2 • 2 • 2 • p • q

29. –25ab2

SOLUTION:  

30. PHOTOGRAPHS Jacy has 24 photographs to put in a rectangular arrangement. In how many different numbers of rows and columns can she display them if each row has the same number of photographs? Name each arrangement.

SOLUTION:  List the different numbers of rows and columns by listing the factors of 24. So, Jacy could form rectangles with the following number of rows and columns: 1 • 24, 24 • 1, 2 • 12, 12 • 2, 3 • 8, 8 • 3, 4 • 6, 6 • 4. There are 8 different arrangements.

Find each product or quotient. Express using exponents.

31. 35 • 3

2

SOLUTION:  

32. (–7) • (–7)4

SOLUTION:  

33. m3 • m6

SOLUTION:  

34. x8 • x

SOLUTION:  

35. (2h7)(6h)

SOLUTION:  

36. (5a3)(–6a

4)

SOLUTION:  

37. 

SOLUTION:  

38. 

SOLUTION:  

39. PLANETS Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how

many times farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by thedistance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Write each expression using a positive exponent.

40. 9–4

SOLUTION:  

9–4

=

41. (–10)–2

SOLUTION:  

(–10)–2

=

42. m–5

SOLUTION:  

m–5 =

Write each fraction as an expression using a negative exponent other than –1.

43. 

SOLUTION:  

= 6–3

44. 

SOLUTION:  

or  or 

45. 

SOLUTION:  

46. MEASUREMENT If 1 millimeter is equal to 10–3

meter and 1 nanometer is equal to 10–9

meter, how many nanometers are in 1 millimeter? Write using a positive exponent.

SOLUTION:  To find the number of nanometers in 1 millimeter, divide the number of millimeters in a meter by the number of nanometers in a meter.

So, there are 106 nanometers in 1 millimeter.

Express each number in standard form.

47. 5.82 × 103

SOLUTION:  

48. 9.0 × 10–2

SOLUTION:  

49. 3.4 × 10–4

SOLUTION:  

50. 1.705 × 105

SOLUTION:  

Express each number in scientific notation.51. 379

SOLUTION:  

52. 26,880

SOLUTION:  

53. 0.0014

SOLUTION:  

54. 0.000561

SOLUTION:  

55. SPACE The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Simplify.

56. (26)3

SOLUTION:  

57. (r2)8

SOLUTION:  

58. (3x7)2

SOLUTION:  

59. (–2n4)6

SOLUTION:  

60. (4a9b)

4

SOLUTION:  

61. (5w5x

8)3

SOLUTION:  

62. GEOMETRY Find the area of the square shown below.

SOLUTION:  

Determine whether each graph, equation, or table represents a linear or nonlinear function. Explain.

63. 

SOLUTION:  The graph is a curve, not a straight line. So, it represents a nonlinear function.

64. 

SOLUTION:  The graph is a line. So, it represents a linear function.

65. y = x

SOLUTION:  

The equation y = x represents a linear function, because it is written in the form y = mx + b.

66. y =  + 1

SOLUTION:  

The equation y =  + 1 represents a nonlinear function, because it cannot be written in the form y = mx + b.

67. 

SOLUTION:  As x increases by 1, y decreases by 2. So, this is a linear function.

68. 

SOLUTION:  As x increases by 1, y increases by 10. So, this is a linear function.

69. SCHOOLS A school district’s spending on students over the last five years is represented by the equation y =

325x2 + 0.2x + 1427. Is this equation linear? Explain.

SOLUTION:  

The equation y = 325x2 + 0.2x + 1427 represents a nonlinear function, because it cannot be written in the form y =

mx + b.

Graph each function.

70. y = 3x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x2 (x, y)

–2 y = 3(–2)2 = 12 (–2, 12)

–1 y = 3(–1)2 = 3 (–1, 3)

0 y = 3(0)2 = 0 (0, 0)

1 y = 3(1)2 = 3 (1, 3)

2 y = 3(2)2 = 12 (2, 12)

71. y = –2x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –2x2 (x, y)

–2 y = –2(–2)2 = –8 (–2, –8)

–1 y = –2(–1)2 = –2 (–1, –2)

0 y = –2(0)2 = 0 (0, 0)

1 y = –2(1)2 = –2 (1, –2)

2 y = –2(2)2 = –8 (2, –8)

72. y = x2 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x2 – 4 (x, y)

–2 y = (–2)2 – 4 = 0 (–2, 0)

–1 y = (–1)2 – 4 = –3 (–1, –3)

0 y = 02 – 4 = –4 (0, –4)

1 y = 12 – 4 = –3 (1, –3)

2 y = 22 – 4 = 0 (2, 0)

73. y = –x2 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –x2 + 1 (x, y)

–2 y = –(–2)2 + 1 = –3 (–2, –3)

–1 y = –(–1)2 + 1 = 0 (–1, 0)

0 y = –(0)2 + 1 = 1 (0, 1)

1 y = –(1)2 + 1 = 0 (1, 0)

2 y = –(2)2 + 1 = –3 (2, –3)

74. y = 2x2 + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x2 + 2 (x, y)

–2 y = 2(–2)2 + 2 = 10 (–2, 10)

–1 y = 2(–1)2 + 2 = 4 (–1, 4)

0 y = 2(0)2 + 2 = 2 (0, 2)

1 y = 2(1)2 + 2 = 4 (1, 4)

2 y = 2(2)2 + 2 = 10 (2, 10)

75. y = x2 – 3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x

2 – 3

(x, y)

–2 y = (–2)

2 – 3 = –1

(–2, –1)

–1 y = (–1)

2 – 3 = –2.5

(–1, –2.5)

0 y = (0)

2 – 3 = –3

(0, –3)

1 y = (1)

2 – 3 = –2.5

(1, –2.5)

2 y = (2)

2 – 3 = –1

(2, –1)

76. GEOMETRY The volume of a cylinder with a height of 8 inches can be found using the equation V = 8(3.14)r2

where r is the radius of the cylinder. Graph the equation.

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

r V = 8(3.14)r2 (r, V)

0 V = 8(3.14)(02) = 0 (0, 0)

1 V = 8(3.14)(12) = 25.12 (1, 25.12)

2 V = 8(3.14)(22) = 100.48 (2, 100.48)

3 V = 8(3.14)(32) = 226.08 (3, 226.08)

4 V = 8(3.14)(42) = 401.92 (4, 401.92)

Graph each function.

77. y = x3 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 + 1 (x, y)

–2 y = (–2)3 + 1 = –7 (–2, –7)

–1 y = (–1)3 + 1 = 0 (–1, 0)

0 y = 03 + 1 = 1 (0, 1)

1 y = 13 + 1 = 2 (1, 2)

2 y = 23 + 1 = 9 (2, 9)

78. y = –3x3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –3x3 (x, y)

–2 y = –3(–2)3 = 24 (–2, 24)

–1 y = –3(–1)3 = 3 (–1, 3)

0 y = –3(0)3 = 0 (0, 0)

1 y = –3(1)3 = –3 (1, –3)

2 y = –3(2)3 = –24 (2, –24)

79. y = x3 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 – 4 (x, y)

–2 y = (–2)3 – 4 = –12 (–2, –12)

–1 y = (–1)3 – 4 = –5 (–1, –5)

0 y = 03 – 4 = –4 (0, –4)

1 y = 13 – 4 = –3 (1, –3)

2 y = 23 – 4 = 4 (2, 4)

80. y = 2x + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x + 2 (x, y)

–2 y = 2–2

+ 2 = 2.25 (–2, 2.25)

–1 y = 2–1

+ 2 = 2.5 (–1, 2.5)

0 y = 20+ 2 = 3 (0, 3)

1 y = 21 + 2 = 4 (1, 4)

2 y = 22 + 2 = 6 (2, 6)

81. y = 3x

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x (x, y)

–2 y = 3

–2 =

(–2, )

–1 y = 3

–1 =

(–1, )

0 y = 30 = 1 (0, 1)

1 y = 31 = 3 (1, 3)

2 y = 32 = 9 (2, 9)

82. y = 2x – 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x – 1 (x, y)

–2 y = 2–2

– 1 = –0.75 (–2, –0.75)

–1 y = 2–1

– 1 = –0.5 (–1, –0.5)

0 y = 20 – 1 = 0 (0, 0)

1 y = 21 – 1 = 1 (1, 1)

2 y = 22 – 1 = 3 (2, 3)

83. LIFE SCIENCE Starting from a single bacterium in a dish, the number of bacteria after t cycles of reproduction is

2t. A bacterium reproduces every 30 minutes. If there are 1000 bacteria in a dish now, how many will there be in 1

hour?

SOLUTION:  

To find the number of bacteria will be in the dish in 1 hour, replace t with 2 in the expression 2t because there are 2

thirty minute cycles in 2 hour. Then, multiply the result by 1000 because there are 1000 bacteria in the dish now.

So, there will be 4000 bacteria in the dish in 1 hour.

eSolutions Manual - Powered by Cognero Page 2

Study Guide and Review

Determine whether each statement is true or false . If false , replace the underlined word or number to make a true statement.

1. The exponent of a number raised to the first power can be omitted.

SOLUTION:  An exponent tells how many times a number is used as a factor. So, the exponent of a number raised to the first power can be omitted. The statement is true.

2. A number is in scientific notation when it does not contain exponents.

SOLUTION:  A number that is expressed as a product of a factor and a power of 10 is written in scientific notation. So, the statement is false. A number is in standard form when it does not contain exponents.

3. In 57, the number 7 is the base.

SOLUTION:  

The number that is multiplied is called the base. So, the statement is false. In 57, the number 7 is the exponent.

4. The number 49 is an example of a(n) prime number.

SOLUTION:  A prime number is a whole number that has exactly two unique factors, 1 and itself. So, the statement is false. The number 49 is an example of a composite number.

5. The equation y = 5x + 2 is an example of a(n) exponential function.

SOLUTION:  

An exponential function is a function that can be described by an equation of the form y = ax + c, where a ≠ 0 and 

a ≠ 1. So, the statement is true.

6. The graph of a(n) cubic function is called a parabola.

SOLUTION:  The statement is false. The graph of a quadratic function is called a parabola.

7. To multiply powers with the same base, add the exponents.

SOLUTION:  The statement is true.

8. A(n) nonlinear function has a constant rate of change.

SOLUTION:  Nonlinear functions do not have constant rates of change. So, the statement is false. A linear function has a constant rate of change.

9. To simplify (n6)5, the first step is to add 6 and 5.

SOLUTION:  

To find the power of a power, multiply exponents. So, the statement is false. To simplify (n6)5, the first step is to

multiply 6 and 5.

10. The graph of a(n) quadratic function is symmetric.

SOLUTION:  The graph of a quadratic function is a parabola, which is symmetric. So, the statement is true.

Write each expression using exponents.11. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

12. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

13. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

14. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

15. 35

SOLUTION:  

16. 2 • 43

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

17. x2 – 6

SOLUTION:  

18. w3 + y2

SOLUTION:  

19. 2(y + z3)

SOLUTION:  

20. w4x

2yz

SOLUTION:  

21. TEETH Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

Write the prime factorization of each number. Use exponents for repeated factors.22. 34

SOLUTION:  34 = 2 • 17

23. 40

SOLUTION:  

24. 63

SOLUTION:  

25. 225

SOLUTION:  

Factor each monomial.26. 18x

SOLUTION:  18x = 2 • 3 • 3 • x

27. 10r2

SOLUTION:  

28. 32pq

SOLUTION:  32pq = 2 • 2 • 2 • 2 • 2 • p • q

29. –25ab2

SOLUTION:  

30. PHOTOGRAPHS Jacy has 24 photographs to put in a rectangular arrangement. In how many different numbers of rows and columns can she display them if each row has the same number of photographs? Name each arrangement.

SOLUTION:  List the different numbers of rows and columns by listing the factors of 24. So, Jacy could form rectangles with the following number of rows and columns: 1 • 24, 24 • 1, 2 • 12, 12 • 2, 3 • 8, 8 • 3, 4 • 6, 6 • 4. There are 8 different arrangements.

Find each product or quotient. Express using exponents.

31. 35 • 3

2

SOLUTION:  

32. (–7) • (–7)4

SOLUTION:  

33. m3 • m6

SOLUTION:  

34. x8 • x

SOLUTION:  

35. (2h7)(6h)

SOLUTION:  

36. (5a3)(–6a

4)

SOLUTION:  

37. 

SOLUTION:  

38. 

SOLUTION:  

39. PLANETS Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how

many times farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by thedistance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Write each expression using a positive exponent.

40. 9–4

SOLUTION:  

9–4

=

41. (–10)–2

SOLUTION:  

(–10)–2

=

42. m–5

SOLUTION:  

m–5 =

Write each fraction as an expression using a negative exponent other than –1.

43. 

SOLUTION:  

= 6–3

44. 

SOLUTION:  

or  or 

45. 

SOLUTION:  

46. MEASUREMENT If 1 millimeter is equal to 10–3

meter and 1 nanometer is equal to 10–9

meter, how many nanometers are in 1 millimeter? Write using a positive exponent.

SOLUTION:  To find the number of nanometers in 1 millimeter, divide the number of millimeters in a meter by the number of nanometers in a meter.

So, there are 106 nanometers in 1 millimeter.

Express each number in standard form.

47. 5.82 × 103

SOLUTION:  

48. 9.0 × 10–2

SOLUTION:  

49. 3.4 × 10–4

SOLUTION:  

50. 1.705 × 105

SOLUTION:  

Express each number in scientific notation.51. 379

SOLUTION:  

52. 26,880

SOLUTION:  

53. 0.0014

SOLUTION:  

54. 0.000561

SOLUTION:  

55. SPACE The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Simplify.

56. (26)3

SOLUTION:  

57. (r2)8

SOLUTION:  

58. (3x7)2

SOLUTION:  

59. (–2n4)6

SOLUTION:  

60. (4a9b)

4

SOLUTION:  

61. (5w5x

8)3

SOLUTION:  

62. GEOMETRY Find the area of the square shown below.

SOLUTION:  

Determine whether each graph, equation, or table represents a linear or nonlinear function. Explain.

63. 

SOLUTION:  The graph is a curve, not a straight line. So, it represents a nonlinear function.

64. 

SOLUTION:  The graph is a line. So, it represents a linear function.

65. y = x

SOLUTION:  

The equation y = x represents a linear function, because it is written in the form y = mx + b.

66. y =  + 1

SOLUTION:  

The equation y =  + 1 represents a nonlinear function, because it cannot be written in the form y = mx + b.

67. 

SOLUTION:  As x increases by 1, y decreases by 2. So, this is a linear function.

68. 

SOLUTION:  As x increases by 1, y increases by 10. So, this is a linear function.

69. SCHOOLS A school district’s spending on students over the last five years is represented by the equation y =

325x2 + 0.2x + 1427. Is this equation linear? Explain.

SOLUTION:  

The equation y = 325x2 + 0.2x + 1427 represents a nonlinear function, because it cannot be written in the form y =

mx + b.

Graph each function.

70. y = 3x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x2 (x, y)

–2 y = 3(–2)2 = 12 (–2, 12)

–1 y = 3(–1)2 = 3 (–1, 3)

0 y = 3(0)2 = 0 (0, 0)

1 y = 3(1)2 = 3 (1, 3)

2 y = 3(2)2 = 12 (2, 12)

71. y = –2x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –2x2 (x, y)

–2 y = –2(–2)2 = –8 (–2, –8)

–1 y = –2(–1)2 = –2 (–1, –2)

0 y = –2(0)2 = 0 (0, 0)

1 y = –2(1)2 = –2 (1, –2)

2 y = –2(2)2 = –8 (2, –8)

72. y = x2 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x2 – 4 (x, y)

–2 y = (–2)2 – 4 = 0 (–2, 0)

–1 y = (–1)2 – 4 = –3 (–1, –3)

0 y = 02 – 4 = –4 (0, –4)

1 y = 12 – 4 = –3 (1, –3)

2 y = 22 – 4 = 0 (2, 0)

73. y = –x2 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –x2 + 1 (x, y)

–2 y = –(–2)2 + 1 = –3 (–2, –3)

–1 y = –(–1)2 + 1 = 0 (–1, 0)

0 y = –(0)2 + 1 = 1 (0, 1)

1 y = –(1)2 + 1 = 0 (1, 0)

2 y = –(2)2 + 1 = –3 (2, –3)

74. y = 2x2 + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x2 + 2 (x, y)

–2 y = 2(–2)2 + 2 = 10 (–2, 10)

–1 y = 2(–1)2 + 2 = 4 (–1, 4)

0 y = 2(0)2 + 2 = 2 (0, 2)

1 y = 2(1)2 + 2 = 4 (1, 4)

2 y = 2(2)2 + 2 = 10 (2, 10)

75. y = x2 – 3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x

2 – 3

(x, y)

–2 y = (–2)

2 – 3 = –1

(–2, –1)

–1 y = (–1)

2 – 3 = –2.5

(–1, –2.5)

0 y = (0)

2 – 3 = –3

(0, –3)

1 y = (1)

2 – 3 = –2.5

(1, –2.5)

2 y = (2)

2 – 3 = –1

(2, –1)

76. GEOMETRY The volume of a cylinder with a height of 8 inches can be found using the equation V = 8(3.14)r2

where r is the radius of the cylinder. Graph the equation.

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

r V = 8(3.14)r2 (r, V)

0 V = 8(3.14)(02) = 0 (0, 0)

1 V = 8(3.14)(12) = 25.12 (1, 25.12)

2 V = 8(3.14)(22) = 100.48 (2, 100.48)

3 V = 8(3.14)(32) = 226.08 (3, 226.08)

4 V = 8(3.14)(42) = 401.92 (4, 401.92)

Graph each function.

77. y = x3 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 + 1 (x, y)

–2 y = (–2)3 + 1 = –7 (–2, –7)

–1 y = (–1)3 + 1 = 0 (–1, 0)

0 y = 03 + 1 = 1 (0, 1)

1 y = 13 + 1 = 2 (1, 2)

2 y = 23 + 1 = 9 (2, 9)

78. y = –3x3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –3x3 (x, y)

–2 y = –3(–2)3 = 24 (–2, 24)

–1 y = –3(–1)3 = 3 (–1, 3)

0 y = –3(0)3 = 0 (0, 0)

1 y = –3(1)3 = –3 (1, –3)

2 y = –3(2)3 = –24 (2, –24)

79. y = x3 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 – 4 (x, y)

–2 y = (–2)3 – 4 = –12 (–2, –12)

–1 y = (–1)3 – 4 = –5 (–1, –5)

0 y = 03 – 4 = –4 (0, –4)

1 y = 13 – 4 = –3 (1, –3)

2 y = 23 – 4 = 4 (2, 4)

80. y = 2x + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x + 2 (x, y)

–2 y = 2–2

+ 2 = 2.25 (–2, 2.25)

–1 y = 2–1

+ 2 = 2.5 (–1, 2.5)

0 y = 20+ 2 = 3 (0, 3)

1 y = 21 + 2 = 4 (1, 4)

2 y = 22 + 2 = 6 (2, 6)

81. y = 3x

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x (x, y)

–2 y = 3

–2 =

(–2, )

–1 y = 3

–1 =

(–1, )

0 y = 30 = 1 (0, 1)

1 y = 31 = 3 (1, 3)

2 y = 32 = 9 (2, 9)

82. y = 2x – 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x – 1 (x, y)

–2 y = 2–2

– 1 = –0.75 (–2, –0.75)

–1 y = 2–1

– 1 = –0.5 (–1, –0.5)

0 y = 20 – 1 = 0 (0, 0)

1 y = 21 – 1 = 1 (1, 1)

2 y = 22 – 1 = 3 (2, 3)

83. LIFE SCIENCE Starting from a single bacterium in a dish, the number of bacteria after t cycles of reproduction is

2t. A bacterium reproduces every 30 minutes. If there are 1000 bacteria in a dish now, how many will there be in 1

hour?

SOLUTION:  

To find the number of bacteria will be in the dish in 1 hour, replace t with 2 in the expression 2t because there are 2

thirty minute cycles in 2 hour. Then, multiply the result by 1000 because there are 1000 bacteria in the dish now.

So, there will be 4000 bacteria in the dish in 1 hour.

eSolutions Manual - Powered by Cognero Page 3

Study Guide and Review

Determine whether each statement is true or false . If false , replace the underlined word or number to make a true statement.

1. The exponent of a number raised to the first power can be omitted.

SOLUTION:  An exponent tells how many times a number is used as a factor. So, the exponent of a number raised to the first power can be omitted. The statement is true.

2. A number is in scientific notation when it does not contain exponents.

SOLUTION:  A number that is expressed as a product of a factor and a power of 10 is written in scientific notation. So, the statement is false. A number is in standard form when it does not contain exponents.

3. In 57, the number 7 is the base.

SOLUTION:  

The number that is multiplied is called the base. So, the statement is false. In 57, the number 7 is the exponent.

4. The number 49 is an example of a(n) prime number.

SOLUTION:  A prime number is a whole number that has exactly two unique factors, 1 and itself. So, the statement is false. The number 49 is an example of a composite number.

5. The equation y = 5x + 2 is an example of a(n) exponential function.

SOLUTION:  

An exponential function is a function that can be described by an equation of the form y = ax + c, where a ≠ 0 and 

a ≠ 1. So, the statement is true.

6. The graph of a(n) cubic function is called a parabola.

SOLUTION:  The statement is false. The graph of a quadratic function is called a parabola.

7. To multiply powers with the same base, add the exponents.

SOLUTION:  The statement is true.

8. A(n) nonlinear function has a constant rate of change.

SOLUTION:  Nonlinear functions do not have constant rates of change. So, the statement is false. A linear function has a constant rate of change.

9. To simplify (n6)5, the first step is to add 6 and 5.

SOLUTION:  

To find the power of a power, multiply exponents. So, the statement is false. To simplify (n6)5, the first step is to

multiply 6 and 5.

10. The graph of a(n) quadratic function is symmetric.

SOLUTION:  The graph of a quadratic function is a parabola, which is symmetric. So, the statement is true.

Write each expression using exponents.11. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

12. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

13. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

14. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

15. 35

SOLUTION:  

16. 2 • 43

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

17. x2 – 6

SOLUTION:  

18. w3 + y2

SOLUTION:  

19. 2(y + z3)

SOLUTION:  

20. w4x

2yz

SOLUTION:  

21. TEETH Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

Write the prime factorization of each number. Use exponents for repeated factors.22. 34

SOLUTION:  34 = 2 • 17

23. 40

SOLUTION:  

24. 63

SOLUTION:  

25. 225

SOLUTION:  

Factor each monomial.26. 18x

SOLUTION:  18x = 2 • 3 • 3 • x

27. 10r2

SOLUTION:  

28. 32pq

SOLUTION:  32pq = 2 • 2 • 2 • 2 • 2 • p • q

29. –25ab2

SOLUTION:  

30. PHOTOGRAPHS Jacy has 24 photographs to put in a rectangular arrangement. In how many different numbers of rows and columns can she display them if each row has the same number of photographs? Name each arrangement.

SOLUTION:  List the different numbers of rows and columns by listing the factors of 24. So, Jacy could form rectangles with the following number of rows and columns: 1 • 24, 24 • 1, 2 • 12, 12 • 2, 3 • 8, 8 • 3, 4 • 6, 6 • 4. There are 8 different arrangements.

Find each product or quotient. Express using exponents.

31. 35 • 3

2

SOLUTION:  

32. (–7) • (–7)4

SOLUTION:  

33. m3 • m6

SOLUTION:  

34. x8 • x

SOLUTION:  

35. (2h7)(6h)

SOLUTION:  

36. (5a3)(–6a

4)

SOLUTION:  

37. 

SOLUTION:  

38. 

SOLUTION:  

39. PLANETS Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how

many times farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by thedistance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Write each expression using a positive exponent.

40. 9–4

SOLUTION:  

9–4

=

41. (–10)–2

SOLUTION:  

(–10)–2

=

42. m–5

SOLUTION:  

m–5 =

Write each fraction as an expression using a negative exponent other than –1.

43. 

SOLUTION:  

= 6–3

44. 

SOLUTION:  

or  or 

45. 

SOLUTION:  

46. MEASUREMENT If 1 millimeter is equal to 10–3

meter and 1 nanometer is equal to 10–9

meter, how many nanometers are in 1 millimeter? Write using a positive exponent.

SOLUTION:  To find the number of nanometers in 1 millimeter, divide the number of millimeters in a meter by the number of nanometers in a meter.

So, there are 106 nanometers in 1 millimeter.

Express each number in standard form.

47. 5.82 × 103

SOLUTION:  

48. 9.0 × 10–2

SOLUTION:  

49. 3.4 × 10–4

SOLUTION:  

50. 1.705 × 105

SOLUTION:  

Express each number in scientific notation.51. 379

SOLUTION:  

52. 26,880

SOLUTION:  

53. 0.0014

SOLUTION:  

54. 0.000561

SOLUTION:  

55. SPACE The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Simplify.

56. (26)3

SOLUTION:  

57. (r2)8

SOLUTION:  

58. (3x7)2

SOLUTION:  

59. (–2n4)6

SOLUTION:  

60. (4a9b)

4

SOLUTION:  

61. (5w5x

8)3

SOLUTION:  

62. GEOMETRY Find the area of the square shown below.

SOLUTION:  

Determine whether each graph, equation, or table represents a linear or nonlinear function. Explain.

63. 

SOLUTION:  The graph is a curve, not a straight line. So, it represents a nonlinear function.

64. 

SOLUTION:  The graph is a line. So, it represents a linear function.

65. y = x

SOLUTION:  

The equation y = x represents a linear function, because it is written in the form y = mx + b.

66. y =  + 1

SOLUTION:  

The equation y =  + 1 represents a nonlinear function, because it cannot be written in the form y = mx + b.

67. 

SOLUTION:  As x increases by 1, y decreases by 2. So, this is a linear function.

68. 

SOLUTION:  As x increases by 1, y increases by 10. So, this is a linear function.

69. SCHOOLS A school district’s spending on students over the last five years is represented by the equation y =

325x2 + 0.2x + 1427. Is this equation linear? Explain.

SOLUTION:  

The equation y = 325x2 + 0.2x + 1427 represents a nonlinear function, because it cannot be written in the form y =

mx + b.

Graph each function.

70. y = 3x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x2 (x, y)

–2 y = 3(–2)2 = 12 (–2, 12)

–1 y = 3(–1)2 = 3 (–1, 3)

0 y = 3(0)2 = 0 (0, 0)

1 y = 3(1)2 = 3 (1, 3)

2 y = 3(2)2 = 12 (2, 12)

71. y = –2x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –2x2 (x, y)

–2 y = –2(–2)2 = –8 (–2, –8)

–1 y = –2(–1)2 = –2 (–1, –2)

0 y = –2(0)2 = 0 (0, 0)

1 y = –2(1)2 = –2 (1, –2)

2 y = –2(2)2 = –8 (2, –8)

72. y = x2 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x2 – 4 (x, y)

–2 y = (–2)2 – 4 = 0 (–2, 0)

–1 y = (–1)2 – 4 = –3 (–1, –3)

0 y = 02 – 4 = –4 (0, –4)

1 y = 12 – 4 = –3 (1, –3)

2 y = 22 – 4 = 0 (2, 0)

73. y = –x2 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –x2 + 1 (x, y)

–2 y = –(–2)2 + 1 = –3 (–2, –3)

–1 y = –(–1)2 + 1 = 0 (–1, 0)

0 y = –(0)2 + 1 = 1 (0, 1)

1 y = –(1)2 + 1 = 0 (1, 0)

2 y = –(2)2 + 1 = –3 (2, –3)

74. y = 2x2 + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x2 + 2 (x, y)

–2 y = 2(–2)2 + 2 = 10 (–2, 10)

–1 y = 2(–1)2 + 2 = 4 (–1, 4)

0 y = 2(0)2 + 2 = 2 (0, 2)

1 y = 2(1)2 + 2 = 4 (1, 4)

2 y = 2(2)2 + 2 = 10 (2, 10)

75. y = x2 – 3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x

2 – 3

(x, y)

–2 y = (–2)

2 – 3 = –1

(–2, –1)

–1 y = (–1)

2 – 3 = –2.5

(–1, –2.5)

0 y = (0)

2 – 3 = –3

(0, –3)

1 y = (1)

2 – 3 = –2.5

(1, –2.5)

2 y = (2)

2 – 3 = –1

(2, –1)

76. GEOMETRY The volume of a cylinder with a height of 8 inches can be found using the equation V = 8(3.14)r2

where r is the radius of the cylinder. Graph the equation.

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

r V = 8(3.14)r2 (r, V)

0 V = 8(3.14)(02) = 0 (0, 0)

1 V = 8(3.14)(12) = 25.12 (1, 25.12)

2 V = 8(3.14)(22) = 100.48 (2, 100.48)

3 V = 8(3.14)(32) = 226.08 (3, 226.08)

4 V = 8(3.14)(42) = 401.92 (4, 401.92)

Graph each function.

77. y = x3 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 + 1 (x, y)

–2 y = (–2)3 + 1 = –7 (–2, –7)

–1 y = (–1)3 + 1 = 0 (–1, 0)

0 y = 03 + 1 = 1 (0, 1)

1 y = 13 + 1 = 2 (1, 2)

2 y = 23 + 1 = 9 (2, 9)

78. y = –3x3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –3x3 (x, y)

–2 y = –3(–2)3 = 24 (–2, 24)

–1 y = –3(–1)3 = 3 (–1, 3)

0 y = –3(0)3 = 0 (0, 0)

1 y = –3(1)3 = –3 (1, –3)

2 y = –3(2)3 = –24 (2, –24)

79. y = x3 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 – 4 (x, y)

–2 y = (–2)3 – 4 = –12 (–2, –12)

–1 y = (–1)3 – 4 = –5 (–1, –5)

0 y = 03 – 4 = –4 (0, –4)

1 y = 13 – 4 = –3 (1, –3)

2 y = 23 – 4 = 4 (2, 4)

80. y = 2x + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x + 2 (x, y)

–2 y = 2–2

+ 2 = 2.25 (–2, 2.25)

–1 y = 2–1

+ 2 = 2.5 (–1, 2.5)

0 y = 20+ 2 = 3 (0, 3)

1 y = 21 + 2 = 4 (1, 4)

2 y = 22 + 2 = 6 (2, 6)

81. y = 3x

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x (x, y)

–2 y = 3

–2 =

(–2, )

–1 y = 3

–1 =

(–1, )

0 y = 30 = 1 (0, 1)

1 y = 31 = 3 (1, 3)

2 y = 32 = 9 (2, 9)

82. y = 2x – 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x – 1 (x, y)

–2 y = 2–2

– 1 = –0.75 (–2, –0.75)

–1 y = 2–1

– 1 = –0.5 (–1, –0.5)

0 y = 20 – 1 = 0 (0, 0)

1 y = 21 – 1 = 1 (1, 1)

2 y = 22 – 1 = 3 (2, 3)

83. LIFE SCIENCE Starting from a single bacterium in a dish, the number of bacteria after t cycles of reproduction is

2t. A bacterium reproduces every 30 minutes. If there are 1000 bacteria in a dish now, how many will there be in 1

hour?

SOLUTION:  

To find the number of bacteria will be in the dish in 1 hour, replace t with 2 in the expression 2t because there are 2

thirty minute cycles in 2 hour. Then, multiply the result by 1000 because there are 1000 bacteria in the dish now.

So, there will be 4000 bacteria in the dish in 1 hour.

eSolutions Manual - Powered by Cognero Page 4

Study Guide and Review

Determine whether each statement is true or false . If false , replace the underlined word or number to make a true statement.

1. The exponent of a number raised to the first power can be omitted.

SOLUTION:  An exponent tells how many times a number is used as a factor. So, the exponent of a number raised to the first power can be omitted. The statement is true.

2. A number is in scientific notation when it does not contain exponents.

SOLUTION:  A number that is expressed as a product of a factor and a power of 10 is written in scientific notation. So, the statement is false. A number is in standard form when it does not contain exponents.

3. In 57, the number 7 is the base.

SOLUTION:  

The number that is multiplied is called the base. So, the statement is false. In 57, the number 7 is the exponent.

4. The number 49 is an example of a(n) prime number.

SOLUTION:  A prime number is a whole number that has exactly two unique factors, 1 and itself. So, the statement is false. The number 49 is an example of a composite number.

5. The equation y = 5x + 2 is an example of a(n) exponential function.

SOLUTION:  

An exponential function is a function that can be described by an equation of the form y = ax + c, where a ≠ 0 and 

a ≠ 1. So, the statement is true.

6. The graph of a(n) cubic function is called a parabola.

SOLUTION:  The statement is false. The graph of a quadratic function is called a parabola.

7. To multiply powers with the same base, add the exponents.

SOLUTION:  The statement is true.

8. A(n) nonlinear function has a constant rate of change.

SOLUTION:  Nonlinear functions do not have constant rates of change. So, the statement is false. A linear function has a constant rate of change.

9. To simplify (n6)5, the first step is to add 6 and 5.

SOLUTION:  

To find the power of a power, multiply exponents. So, the statement is false. To simplify (n6)5, the first step is to

multiply 6 and 5.

10. The graph of a(n) quadratic function is symmetric.

SOLUTION:  The graph of a quadratic function is a parabola, which is symmetric. So, the statement is true.

Write each expression using exponents.11. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

12. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

13. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

14. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

15. 35

SOLUTION:  

16. 2 • 43

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

17. x2 – 6

SOLUTION:  

18. w3 + y2

SOLUTION:  

19. 2(y + z3)

SOLUTION:  

20. w4x

2yz

SOLUTION:  

21. TEETH Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

Write the prime factorization of each number. Use exponents for repeated factors.22. 34

SOLUTION:  34 = 2 • 17

23. 40

SOLUTION:  

24. 63

SOLUTION:  

25. 225

SOLUTION:  

Factor each monomial.26. 18x

SOLUTION:  18x = 2 • 3 • 3 • x

27. 10r2

SOLUTION:  

28. 32pq

SOLUTION:  32pq = 2 • 2 • 2 • 2 • 2 • p • q

29. –25ab2

SOLUTION:  

30. PHOTOGRAPHS Jacy has 24 photographs to put in a rectangular arrangement. In how many different numbers of rows and columns can she display them if each row has the same number of photographs? Name each arrangement.

SOLUTION:  List the different numbers of rows and columns by listing the factors of 24. So, Jacy could form rectangles with the following number of rows and columns: 1 • 24, 24 • 1, 2 • 12, 12 • 2, 3 • 8, 8 • 3, 4 • 6, 6 • 4. There are 8 different arrangements.

Find each product or quotient. Express using exponents.

31. 35 • 3

2

SOLUTION:  

32. (–7) • (–7)4

SOLUTION:  

33. m3 • m6

SOLUTION:  

34. x8 • x

SOLUTION:  

35. (2h7)(6h)

SOLUTION:  

36. (5a3)(–6a

4)

SOLUTION:  

37. 

SOLUTION:  

38. 

SOLUTION:  

39. PLANETS Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how

many times farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by thedistance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Write each expression using a positive exponent.

40. 9–4

SOLUTION:  

9–4

=

41. (–10)–2

SOLUTION:  

(–10)–2

=

42. m–5

SOLUTION:  

m–5 =

Write each fraction as an expression using a negative exponent other than –1.

43. 

SOLUTION:  

= 6–3

44. 

SOLUTION:  

or  or 

45. 

SOLUTION:  

46. MEASUREMENT If 1 millimeter is equal to 10–3

meter and 1 nanometer is equal to 10–9

meter, how many nanometers are in 1 millimeter? Write using a positive exponent.

SOLUTION:  To find the number of nanometers in 1 millimeter, divide the number of millimeters in a meter by the number of nanometers in a meter.

So, there are 106 nanometers in 1 millimeter.

Express each number in standard form.

47. 5.82 × 103

SOLUTION:  

48. 9.0 × 10–2

SOLUTION:  

49. 3.4 × 10–4

SOLUTION:  

50. 1.705 × 105

SOLUTION:  

Express each number in scientific notation.51. 379

SOLUTION:  

52. 26,880

SOLUTION:  

53. 0.0014

SOLUTION:  

54. 0.000561

SOLUTION:  

55. SPACE The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Simplify.

56. (26)3

SOLUTION:  

57. (r2)8

SOLUTION:  

58. (3x7)2

SOLUTION:  

59. (–2n4)6

SOLUTION:  

60. (4a9b)

4

SOLUTION:  

61. (5w5x

8)3

SOLUTION:  

62. GEOMETRY Find the area of the square shown below.

SOLUTION:  

Determine whether each graph, equation, or table represents a linear or nonlinear function. Explain.

63. 

SOLUTION:  The graph is a curve, not a straight line. So, it represents a nonlinear function.

64. 

SOLUTION:  The graph is a line. So, it represents a linear function.

65. y = x

SOLUTION:  

The equation y = x represents a linear function, because it is written in the form y = mx + b.

66. y =  + 1

SOLUTION:  

The equation y =  + 1 represents a nonlinear function, because it cannot be written in the form y = mx + b.

67. 

SOLUTION:  As x increases by 1, y decreases by 2. So, this is a linear function.

68. 

SOLUTION:  As x increases by 1, y increases by 10. So, this is a linear function.

69. SCHOOLS A school district’s spending on students over the last five years is represented by the equation y =

325x2 + 0.2x + 1427. Is this equation linear? Explain.

SOLUTION:  

The equation y = 325x2 + 0.2x + 1427 represents a nonlinear function, because it cannot be written in the form y =

mx + b.

Graph each function.

70. y = 3x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x2 (x, y)

–2 y = 3(–2)2 = 12 (–2, 12)

–1 y = 3(–1)2 = 3 (–1, 3)

0 y = 3(0)2 = 0 (0, 0)

1 y = 3(1)2 = 3 (1, 3)

2 y = 3(2)2 = 12 (2, 12)

71. y = –2x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –2x2 (x, y)

–2 y = –2(–2)2 = –8 (–2, –8)

–1 y = –2(–1)2 = –2 (–1, –2)

0 y = –2(0)2 = 0 (0, 0)

1 y = –2(1)2 = –2 (1, –2)

2 y = –2(2)2 = –8 (2, –8)

72. y = x2 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x2 – 4 (x, y)

–2 y = (–2)2 – 4 = 0 (–2, 0)

–1 y = (–1)2 – 4 = –3 (–1, –3)

0 y = 02 – 4 = –4 (0, –4)

1 y = 12 – 4 = –3 (1, –3)

2 y = 22 – 4 = 0 (2, 0)

73. y = –x2 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –x2 + 1 (x, y)

–2 y = –(–2)2 + 1 = –3 (–2, –3)

–1 y = –(–1)2 + 1 = 0 (–1, 0)

0 y = –(0)2 + 1 = 1 (0, 1)

1 y = –(1)2 + 1 = 0 (1, 0)

2 y = –(2)2 + 1 = –3 (2, –3)

74. y = 2x2 + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x2 + 2 (x, y)

–2 y = 2(–2)2 + 2 = 10 (–2, 10)

–1 y = 2(–1)2 + 2 = 4 (–1, 4)

0 y = 2(0)2 + 2 = 2 (0, 2)

1 y = 2(1)2 + 2 = 4 (1, 4)

2 y = 2(2)2 + 2 = 10 (2, 10)

75. y = x2 – 3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x

2 – 3

(x, y)

–2 y = (–2)

2 – 3 = –1

(–2, –1)

–1 y = (–1)

2 – 3 = –2.5

(–1, –2.5)

0 y = (0)

2 – 3 = –3

(0, –3)

1 y = (1)

2 – 3 = –2.5

(1, –2.5)

2 y = (2)

2 – 3 = –1

(2, –1)

76. GEOMETRY The volume of a cylinder with a height of 8 inches can be found using the equation V = 8(3.14)r2

where r is the radius of the cylinder. Graph the equation.

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

r V = 8(3.14)r2 (r, V)

0 V = 8(3.14)(02) = 0 (0, 0)

1 V = 8(3.14)(12) = 25.12 (1, 25.12)

2 V = 8(3.14)(22) = 100.48 (2, 100.48)

3 V = 8(3.14)(32) = 226.08 (3, 226.08)

4 V = 8(3.14)(42) = 401.92 (4, 401.92)

Graph each function.

77. y = x3 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 + 1 (x, y)

–2 y = (–2)3 + 1 = –7 (–2, –7)

–1 y = (–1)3 + 1 = 0 (–1, 0)

0 y = 03 + 1 = 1 (0, 1)

1 y = 13 + 1 = 2 (1, 2)

2 y = 23 + 1 = 9 (2, 9)

78. y = –3x3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –3x3 (x, y)

–2 y = –3(–2)3 = 24 (–2, 24)

–1 y = –3(–1)3 = 3 (–1, 3)

0 y = –3(0)3 = 0 (0, 0)

1 y = –3(1)3 = –3 (1, –3)

2 y = –3(2)3 = –24 (2, –24)

79. y = x3 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 – 4 (x, y)

–2 y = (–2)3 – 4 = –12 (–2, –12)

–1 y = (–1)3 – 4 = –5 (–1, –5)

0 y = 03 – 4 = –4 (0, –4)

1 y = 13 – 4 = –3 (1, –3)

2 y = 23 – 4 = 4 (2, 4)

80. y = 2x + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x + 2 (x, y)

–2 y = 2–2

+ 2 = 2.25 (–2, 2.25)

–1 y = 2–1

+ 2 = 2.5 (–1, 2.5)

0 y = 20+ 2 = 3 (0, 3)

1 y = 21 + 2 = 4 (1, 4)

2 y = 22 + 2 = 6 (2, 6)

81. y = 3x

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x (x, y)

–2 y = 3

–2 =

(–2, )

–1 y = 3

–1 =

(–1, )

0 y = 30 = 1 (0, 1)

1 y = 31 = 3 (1, 3)

2 y = 32 = 9 (2, 9)

82. y = 2x – 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x – 1 (x, y)

–2 y = 2–2

– 1 = –0.75 (–2, –0.75)

–1 y = 2–1

– 1 = –0.5 (–1, –0.5)

0 y = 20 – 1 = 0 (0, 0)

1 y = 21 – 1 = 1 (1, 1)

2 y = 22 – 1 = 3 (2, 3)

83. LIFE SCIENCE Starting from a single bacterium in a dish, the number of bacteria after t cycles of reproduction is

2t. A bacterium reproduces every 30 minutes. If there are 1000 bacteria in a dish now, how many will there be in 1

hour?

SOLUTION:  

To find the number of bacteria will be in the dish in 1 hour, replace t with 2 in the expression 2t because there are 2

thirty minute cycles in 2 hour. Then, multiply the result by 1000 because there are 1000 bacteria in the dish now.

So, there will be 4000 bacteria in the dish in 1 hour.

eSolutions Manual - Powered by Cognero Page 5

Study Guide and Review

Determine whether each statement is true or false . If false , replace the underlined word or number to make a true statement.

1. The exponent of a number raised to the first power can be omitted.

SOLUTION:  An exponent tells how many times a number is used as a factor. So, the exponent of a number raised to the first power can be omitted. The statement is true.

2. A number is in scientific notation when it does not contain exponents.

SOLUTION:  A number that is expressed as a product of a factor and a power of 10 is written in scientific notation. So, the statement is false. A number is in standard form when it does not contain exponents.

3. In 57, the number 7 is the base.

SOLUTION:  

The number that is multiplied is called the base. So, the statement is false. In 57, the number 7 is the exponent.

4. The number 49 is an example of a(n) prime number.

SOLUTION:  A prime number is a whole number that has exactly two unique factors, 1 and itself. So, the statement is false. The number 49 is an example of a composite number.

5. The equation y = 5x + 2 is an example of a(n) exponential function.

SOLUTION:  

An exponential function is a function that can be described by an equation of the form y = ax + c, where a ≠ 0 and 

a ≠ 1. So, the statement is true.

6. The graph of a(n) cubic function is called a parabola.

SOLUTION:  The statement is false. The graph of a quadratic function is called a parabola.

7. To multiply powers with the same base, add the exponents.

SOLUTION:  The statement is true.

8. A(n) nonlinear function has a constant rate of change.

SOLUTION:  Nonlinear functions do not have constant rates of change. So, the statement is false. A linear function has a constant rate of change.

9. To simplify (n6)5, the first step is to add 6 and 5.

SOLUTION:  

To find the power of a power, multiply exponents. So, the statement is false. To simplify (n6)5, the first step is to

multiply 6 and 5.

10. The graph of a(n) quadratic function is symmetric.

SOLUTION:  The graph of a quadratic function is a parabola, which is symmetric. So, the statement is true.

Write each expression using exponents.11. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

12. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

13. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

14. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

15. 35

SOLUTION:  

16. 2 • 43

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

17. x2 – 6

SOLUTION:  

18. w3 + y2

SOLUTION:  

19. 2(y + z3)

SOLUTION:  

20. w4x

2yz

SOLUTION:  

21. TEETH Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

Write the prime factorization of each number. Use exponents for repeated factors.22. 34

SOLUTION:  34 = 2 • 17

23. 40

SOLUTION:  

24. 63

SOLUTION:  

25. 225

SOLUTION:  

Factor each monomial.26. 18x

SOLUTION:  18x = 2 • 3 • 3 • x

27. 10r2

SOLUTION:  

28. 32pq

SOLUTION:  32pq = 2 • 2 • 2 • 2 • 2 • p • q

29. –25ab2

SOLUTION:  

30. PHOTOGRAPHS Jacy has 24 photographs to put in a rectangular arrangement. In how many different numbers of rows and columns can she display them if each row has the same number of photographs? Name each arrangement.

SOLUTION:  List the different numbers of rows and columns by listing the factors of 24. So, Jacy could form rectangles with the following number of rows and columns: 1 • 24, 24 • 1, 2 • 12, 12 • 2, 3 • 8, 8 • 3, 4 • 6, 6 • 4. There are 8 different arrangements.

Find each product or quotient. Express using exponents.

31. 35 • 3

2

SOLUTION:  

32. (–7) • (–7)4

SOLUTION:  

33. m3 • m6

SOLUTION:  

34. x8 • x

SOLUTION:  

35. (2h7)(6h)

SOLUTION:  

36. (5a3)(–6a

4)

SOLUTION:  

37. 

SOLUTION:  

38. 

SOLUTION:  

39. PLANETS Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how

many times farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by thedistance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Write each expression using a positive exponent.

40. 9–4

SOLUTION:  

9–4

=

41. (–10)–2

SOLUTION:  

(–10)–2

=

42. m–5

SOLUTION:  

m–5 =

Write each fraction as an expression using a negative exponent other than –1.

43. 

SOLUTION:  

= 6–3

44. 

SOLUTION:  

or  or 

45. 

SOLUTION:  

46. MEASUREMENT If 1 millimeter is equal to 10–3

meter and 1 nanometer is equal to 10–9

meter, how many nanometers are in 1 millimeter? Write using a positive exponent.

SOLUTION:  To find the number of nanometers in 1 millimeter, divide the number of millimeters in a meter by the number of nanometers in a meter.

So, there are 106 nanometers in 1 millimeter.

Express each number in standard form.

47. 5.82 × 103

SOLUTION:  

48. 9.0 × 10–2

SOLUTION:  

49. 3.4 × 10–4

SOLUTION:  

50. 1.705 × 105

SOLUTION:  

Express each number in scientific notation.51. 379

SOLUTION:  

52. 26,880

SOLUTION:  

53. 0.0014

SOLUTION:  

54. 0.000561

SOLUTION:  

55. SPACE The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Simplify.

56. (26)3

SOLUTION:  

57. (r2)8

SOLUTION:  

58. (3x7)2

SOLUTION:  

59. (–2n4)6

SOLUTION:  

60. (4a9b)

4

SOLUTION:  

61. (5w5x

8)3

SOLUTION:  

62. GEOMETRY Find the area of the square shown below.

SOLUTION:  

Determine whether each graph, equation, or table represents a linear or nonlinear function. Explain.

63. 

SOLUTION:  The graph is a curve, not a straight line. So, it represents a nonlinear function.

64. 

SOLUTION:  The graph is a line. So, it represents a linear function.

65. y = x

SOLUTION:  

The equation y = x represents a linear function, because it is written in the form y = mx + b.

66. y =  + 1

SOLUTION:  

The equation y =  + 1 represents a nonlinear function, because it cannot be written in the form y = mx + b.

67. 

SOLUTION:  As x increases by 1, y decreases by 2. So, this is a linear function.

68. 

SOLUTION:  As x increases by 1, y increases by 10. So, this is a linear function.

69. SCHOOLS A school district’s spending on students over the last five years is represented by the equation y =

325x2 + 0.2x + 1427. Is this equation linear? Explain.

SOLUTION:  

The equation y = 325x2 + 0.2x + 1427 represents a nonlinear function, because it cannot be written in the form y =

mx + b.

Graph each function.

70. y = 3x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x2 (x, y)

–2 y = 3(–2)2 = 12 (–2, 12)

–1 y = 3(–1)2 = 3 (–1, 3)

0 y = 3(0)2 = 0 (0, 0)

1 y = 3(1)2 = 3 (1, 3)

2 y = 3(2)2 = 12 (2, 12)

71. y = –2x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –2x2 (x, y)

–2 y = –2(–2)2 = –8 (–2, –8)

–1 y = –2(–1)2 = –2 (–1, –2)

0 y = –2(0)2 = 0 (0, 0)

1 y = –2(1)2 = –2 (1, –2)

2 y = –2(2)2 = –8 (2, –8)

72. y = x2 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x2 – 4 (x, y)

–2 y = (–2)2 – 4 = 0 (–2, 0)

–1 y = (–1)2 – 4 = –3 (–1, –3)

0 y = 02 – 4 = –4 (0, –4)

1 y = 12 – 4 = –3 (1, –3)

2 y = 22 – 4 = 0 (2, 0)

73. y = –x2 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –x2 + 1 (x, y)

–2 y = –(–2)2 + 1 = –3 (–2, –3)

–1 y = –(–1)2 + 1 = 0 (–1, 0)

0 y = –(0)2 + 1 = 1 (0, 1)

1 y = –(1)2 + 1 = 0 (1, 0)

2 y = –(2)2 + 1 = –3 (2, –3)

74. y = 2x2 + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x2 + 2 (x, y)

–2 y = 2(–2)2 + 2 = 10 (–2, 10)

–1 y = 2(–1)2 + 2 = 4 (–1, 4)

0 y = 2(0)2 + 2 = 2 (0, 2)

1 y = 2(1)2 + 2 = 4 (1, 4)

2 y = 2(2)2 + 2 = 10 (2, 10)

75. y = x2 – 3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x

2 – 3

(x, y)

–2 y = (–2)

2 – 3 = –1

(–2, –1)

–1 y = (–1)

2 – 3 = –2.5

(–1, –2.5)

0 y = (0)

2 – 3 = –3

(0, –3)

1 y = (1)

2 – 3 = –2.5

(1, –2.5)

2 y = (2)

2 – 3 = –1

(2, –1)

76. GEOMETRY The volume of a cylinder with a height of 8 inches can be found using the equation V = 8(3.14)r2

where r is the radius of the cylinder. Graph the equation.

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

r V = 8(3.14)r2 (r, V)

0 V = 8(3.14)(02) = 0 (0, 0)

1 V = 8(3.14)(12) = 25.12 (1, 25.12)

2 V = 8(3.14)(22) = 100.48 (2, 100.48)

3 V = 8(3.14)(32) = 226.08 (3, 226.08)

4 V = 8(3.14)(42) = 401.92 (4, 401.92)

Graph each function.

77. y = x3 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 + 1 (x, y)

–2 y = (–2)3 + 1 = –7 (–2, –7)

–1 y = (–1)3 + 1 = 0 (–1, 0)

0 y = 03 + 1 = 1 (0, 1)

1 y = 13 + 1 = 2 (1, 2)

2 y = 23 + 1 = 9 (2, 9)

78. y = –3x3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –3x3 (x, y)

–2 y = –3(–2)3 = 24 (–2, 24)

–1 y = –3(–1)3 = 3 (–1, 3)

0 y = –3(0)3 = 0 (0, 0)

1 y = –3(1)3 = –3 (1, –3)

2 y = –3(2)3 = –24 (2, –24)

79. y = x3 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 – 4 (x, y)

–2 y = (–2)3 – 4 = –12 (–2, –12)

–1 y = (–1)3 – 4 = –5 (–1, –5)

0 y = 03 – 4 = –4 (0, –4)

1 y = 13 – 4 = –3 (1, –3)

2 y = 23 – 4 = 4 (2, 4)

80. y = 2x + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x + 2 (x, y)

–2 y = 2–2

+ 2 = 2.25 (–2, 2.25)

–1 y = 2–1

+ 2 = 2.5 (–1, 2.5)

0 y = 20+ 2 = 3 (0, 3)

1 y = 21 + 2 = 4 (1, 4)

2 y = 22 + 2 = 6 (2, 6)

81. y = 3x

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x (x, y)

–2 y = 3

–2 =

(–2, )

–1 y = 3

–1 =

(–1, )

0 y = 30 = 1 (0, 1)

1 y = 31 = 3 (1, 3)

2 y = 32 = 9 (2, 9)

82. y = 2x – 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x – 1 (x, y)

–2 y = 2–2

– 1 = –0.75 (–2, –0.75)

–1 y = 2–1

– 1 = –0.5 (–1, –0.5)

0 y = 20 – 1 = 0 (0, 0)

1 y = 21 – 1 = 1 (1, 1)

2 y = 22 – 1 = 3 (2, 3)

83. LIFE SCIENCE Starting from a single bacterium in a dish, the number of bacteria after t cycles of reproduction is

2t. A bacterium reproduces every 30 minutes. If there are 1000 bacteria in a dish now, how many will there be in 1

hour?

SOLUTION:  

To find the number of bacteria will be in the dish in 1 hour, replace t with 2 in the expression 2t because there are 2

thirty minute cycles in 2 hour. Then, multiply the result by 1000 because there are 1000 bacteria in the dish now.

So, there will be 4000 bacteria in the dish in 1 hour.

eSolutions Manual - Powered by Cognero Page 6

Study Guide and Review

Determine whether each statement is true or false . If false , replace the underlined word or number to make a true statement.

1. The exponent of a number raised to the first power can be omitted.

SOLUTION:  An exponent tells how many times a number is used as a factor. So, the exponent of a number raised to the first power can be omitted. The statement is true.

2. A number is in scientific notation when it does not contain exponents.

SOLUTION:  A number that is expressed as a product of a factor and a power of 10 is written in scientific notation. So, the statement is false. A number is in standard form when it does not contain exponents.

3. In 57, the number 7 is the base.

SOLUTION:  

The number that is multiplied is called the base. So, the statement is false. In 57, the number 7 is the exponent.

4. The number 49 is an example of a(n) prime number.

SOLUTION:  A prime number is a whole number that has exactly two unique factors, 1 and itself. So, the statement is false. The number 49 is an example of a composite number.

5. The equation y = 5x + 2 is an example of a(n) exponential function.

SOLUTION:  

An exponential function is a function that can be described by an equation of the form y = ax + c, where a ≠ 0 and 

a ≠ 1. So, the statement is true.

6. The graph of a(n) cubic function is called a parabola.

SOLUTION:  The statement is false. The graph of a quadratic function is called a parabola.

7. To multiply powers with the same base, add the exponents.

SOLUTION:  The statement is true.

8. A(n) nonlinear function has a constant rate of change.

SOLUTION:  Nonlinear functions do not have constant rates of change. So, the statement is false. A linear function has a constant rate of change.

9. To simplify (n6)5, the first step is to add 6 and 5.

SOLUTION:  

To find the power of a power, multiply exponents. So, the statement is false. To simplify (n6)5, the first step is to

multiply 6 and 5.

10. The graph of a(n) quadratic function is symmetric.

SOLUTION:  The graph of a quadratic function is a parabola, which is symmetric. So, the statement is true.

Write each expression using exponents.11. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

12. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

13. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

14. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

15. 35

SOLUTION:  

16. 2 • 43

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

17. x2 – 6

SOLUTION:  

18. w3 + y2

SOLUTION:  

19. 2(y + z3)

SOLUTION:  

20. w4x

2yz

SOLUTION:  

21. TEETH Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

Write the prime factorization of each number. Use exponents for repeated factors.22. 34

SOLUTION:  34 = 2 • 17

23. 40

SOLUTION:  

24. 63

SOLUTION:  

25. 225

SOLUTION:  

Factor each monomial.26. 18x

SOLUTION:  18x = 2 • 3 • 3 • x

27. 10r2

SOLUTION:  

28. 32pq

SOLUTION:  32pq = 2 • 2 • 2 • 2 • 2 • p • q

29. –25ab2

SOLUTION:  

30. PHOTOGRAPHS Jacy has 24 photographs to put in a rectangular arrangement. In how many different numbers of rows and columns can she display them if each row has the same number of photographs? Name each arrangement.

SOLUTION:  List the different numbers of rows and columns by listing the factors of 24. So, Jacy could form rectangles with the following number of rows and columns: 1 • 24, 24 • 1, 2 • 12, 12 • 2, 3 • 8, 8 • 3, 4 • 6, 6 • 4. There are 8 different arrangements.

Find each product or quotient. Express using exponents.

31. 35 • 3

2

SOLUTION:  

32. (–7) • (–7)4

SOLUTION:  

33. m3 • m6

SOLUTION:  

34. x8 • x

SOLUTION:  

35. (2h7)(6h)

SOLUTION:  

36. (5a3)(–6a

4)

SOLUTION:  

37. 

SOLUTION:  

38. 

SOLUTION:  

39. PLANETS Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how

many times farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by thedistance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Write each expression using a positive exponent.

40. 9–4

SOLUTION:  

9–4

=

41. (–10)–2

SOLUTION:  

(–10)–2

=

42. m–5

SOLUTION:  

m–5 =

Write each fraction as an expression using a negative exponent other than –1.

43. 

SOLUTION:  

= 6–3

44. 

SOLUTION:  

or  or 

45. 

SOLUTION:  

46. MEASUREMENT If 1 millimeter is equal to 10–3

meter and 1 nanometer is equal to 10–9

meter, how many nanometers are in 1 millimeter? Write using a positive exponent.

SOLUTION:  To find the number of nanometers in 1 millimeter, divide the number of millimeters in a meter by the number of nanometers in a meter.

So, there are 106 nanometers in 1 millimeter.

Express each number in standard form.

47. 5.82 × 103

SOLUTION:  

48. 9.0 × 10–2

SOLUTION:  

49. 3.4 × 10–4

SOLUTION:  

50. 1.705 × 105

SOLUTION:  

Express each number in scientific notation.51. 379

SOLUTION:  

52. 26,880

SOLUTION:  

53. 0.0014

SOLUTION:  

54. 0.000561

SOLUTION:  

55. SPACE The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Simplify.

56. (26)3

SOLUTION:  

57. (r2)8

SOLUTION:  

58. (3x7)2

SOLUTION:  

59. (–2n4)6

SOLUTION:  

60. (4a9b)

4

SOLUTION:  

61. (5w5x

8)3

SOLUTION:  

62. GEOMETRY Find the area of the square shown below.

SOLUTION:  

Determine whether each graph, equation, or table represents a linear or nonlinear function. Explain.

63. 

SOLUTION:  The graph is a curve, not a straight line. So, it represents a nonlinear function.

64. 

SOLUTION:  The graph is a line. So, it represents a linear function.

65. y = x

SOLUTION:  

The equation y = x represents a linear function, because it is written in the form y = mx + b.

66. y =  + 1

SOLUTION:  

The equation y =  + 1 represents a nonlinear function, because it cannot be written in the form y = mx + b.

67. 

SOLUTION:  As x increases by 1, y decreases by 2. So, this is a linear function.

68. 

SOLUTION:  As x increases by 1, y increases by 10. So, this is a linear function.

69. SCHOOLS A school district’s spending on students over the last five years is represented by the equation y =

325x2 + 0.2x + 1427. Is this equation linear? Explain.

SOLUTION:  

The equation y = 325x2 + 0.2x + 1427 represents a nonlinear function, because it cannot be written in the form y =

mx + b.

Graph each function.

70. y = 3x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x2 (x, y)

–2 y = 3(–2)2 = 12 (–2, 12)

–1 y = 3(–1)2 = 3 (–1, 3)

0 y = 3(0)2 = 0 (0, 0)

1 y = 3(1)2 = 3 (1, 3)

2 y = 3(2)2 = 12 (2, 12)

71. y = –2x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –2x2 (x, y)

–2 y = –2(–2)2 = –8 (–2, –8)

–1 y = –2(–1)2 = –2 (–1, –2)

0 y = –2(0)2 = 0 (0, 0)

1 y = –2(1)2 = –2 (1, –2)

2 y = –2(2)2 = –8 (2, –8)

72. y = x2 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x2 – 4 (x, y)

–2 y = (–2)2 – 4 = 0 (–2, 0)

–1 y = (–1)2 – 4 = –3 (–1, –3)

0 y = 02 – 4 = –4 (0, –4)

1 y = 12 – 4 = –3 (1, –3)

2 y = 22 – 4 = 0 (2, 0)

73. y = –x2 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –x2 + 1 (x, y)

–2 y = –(–2)2 + 1 = –3 (–2, –3)

–1 y = –(–1)2 + 1 = 0 (–1, 0)

0 y = –(0)2 + 1 = 1 (0, 1)

1 y = –(1)2 + 1 = 0 (1, 0)

2 y = –(2)2 + 1 = –3 (2, –3)

74. y = 2x2 + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x2 + 2 (x, y)

–2 y = 2(–2)2 + 2 = 10 (–2, 10)

–1 y = 2(–1)2 + 2 = 4 (–1, 4)

0 y = 2(0)2 + 2 = 2 (0, 2)

1 y = 2(1)2 + 2 = 4 (1, 4)

2 y = 2(2)2 + 2 = 10 (2, 10)

75. y = x2 – 3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x

2 – 3

(x, y)

–2 y = (–2)

2 – 3 = –1

(–2, –1)

–1 y = (–1)

2 – 3 = –2.5

(–1, –2.5)

0 y = (0)

2 – 3 = –3

(0, –3)

1 y = (1)

2 – 3 = –2.5

(1, –2.5)

2 y = (2)

2 – 3 = –1

(2, –1)

76. GEOMETRY The volume of a cylinder with a height of 8 inches can be found using the equation V = 8(3.14)r2

where r is the radius of the cylinder. Graph the equation.

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

r V = 8(3.14)r2 (r, V)

0 V = 8(3.14)(02) = 0 (0, 0)

1 V = 8(3.14)(12) = 25.12 (1, 25.12)

2 V = 8(3.14)(22) = 100.48 (2, 100.48)

3 V = 8(3.14)(32) = 226.08 (3, 226.08)

4 V = 8(3.14)(42) = 401.92 (4, 401.92)

Graph each function.

77. y = x3 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 + 1 (x, y)

–2 y = (–2)3 + 1 = –7 (–2, –7)

–1 y = (–1)3 + 1 = 0 (–1, 0)

0 y = 03 + 1 = 1 (0, 1)

1 y = 13 + 1 = 2 (1, 2)

2 y = 23 + 1 = 9 (2, 9)

78. y = –3x3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –3x3 (x, y)

–2 y = –3(–2)3 = 24 (–2, 24)

–1 y = –3(–1)3 = 3 (–1, 3)

0 y = –3(0)3 = 0 (0, 0)

1 y = –3(1)3 = –3 (1, –3)

2 y = –3(2)3 = –24 (2, –24)

79. y = x3 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 – 4 (x, y)

–2 y = (–2)3 – 4 = –12 (–2, –12)

–1 y = (–1)3 – 4 = –5 (–1, –5)

0 y = 03 – 4 = –4 (0, –4)

1 y = 13 – 4 = –3 (1, –3)

2 y = 23 – 4 = 4 (2, 4)

80. y = 2x + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x + 2 (x, y)

–2 y = 2–2

+ 2 = 2.25 (–2, 2.25)

–1 y = 2–1

+ 2 = 2.5 (–1, 2.5)

0 y = 20+ 2 = 3 (0, 3)

1 y = 21 + 2 = 4 (1, 4)

2 y = 22 + 2 = 6 (2, 6)

81. y = 3x

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x (x, y)

–2 y = 3

–2 =

(–2, )

–1 y = 3

–1 =

(–1, )

0 y = 30 = 1 (0, 1)

1 y = 31 = 3 (1, 3)

2 y = 32 = 9 (2, 9)

82. y = 2x – 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x – 1 (x, y)

–2 y = 2–2

– 1 = –0.75 (–2, –0.75)

–1 y = 2–1

– 1 = –0.5 (–1, –0.5)

0 y = 20 – 1 = 0 (0, 0)

1 y = 21 – 1 = 1 (1, 1)

2 y = 22 – 1 = 3 (2, 3)

83. LIFE SCIENCE Starting from a single bacterium in a dish, the number of bacteria after t cycles of reproduction is

2t. A bacterium reproduces every 30 minutes. If there are 1000 bacteria in a dish now, how many will there be in 1

hour?

SOLUTION:  

To find the number of bacteria will be in the dish in 1 hour, replace t with 2 in the expression 2t because there are 2

thirty minute cycles in 2 hour. Then, multiply the result by 1000 because there are 1000 bacteria in the dish now.

So, there will be 4000 bacteria in the dish in 1 hour.

eSolutions Manual - Powered by Cognero Page 7

Study Guide and Review

Determine whether each statement is true or false . If false , replace the underlined word or number to make a true statement.

1. The exponent of a number raised to the first power can be omitted.

SOLUTION:  An exponent tells how many times a number is used as a factor. So, the exponent of a number raised to the first power can be omitted. The statement is true.

2. A number is in scientific notation when it does not contain exponents.

SOLUTION:  A number that is expressed as a product of a factor and a power of 10 is written in scientific notation. So, the statement is false. A number is in standard form when it does not contain exponents.

3. In 57, the number 7 is the base.

SOLUTION:  

The number that is multiplied is called the base. So, the statement is false. In 57, the number 7 is the exponent.

4. The number 49 is an example of a(n) prime number.

SOLUTION:  A prime number is a whole number that has exactly two unique factors, 1 and itself. So, the statement is false. The number 49 is an example of a composite number.

5. The equation y = 5x + 2 is an example of a(n) exponential function.

SOLUTION:  

An exponential function is a function that can be described by an equation of the form y = ax + c, where a ≠ 0 and 

a ≠ 1. So, the statement is true.

6. The graph of a(n) cubic function is called a parabola.

SOLUTION:  The statement is false. The graph of a quadratic function is called a parabola.

7. To multiply powers with the same base, add the exponents.

SOLUTION:  The statement is true.

8. A(n) nonlinear function has a constant rate of change.

SOLUTION:  Nonlinear functions do not have constant rates of change. So, the statement is false. A linear function has a constant rate of change.

9. To simplify (n6)5, the first step is to add 6 and 5.

SOLUTION:  

To find the power of a power, multiply exponents. So, the statement is false. To simplify (n6)5, the first step is to

multiply 6 and 5.

10. The graph of a(n) quadratic function is symmetric.

SOLUTION:  The graph of a quadratic function is a parabola, which is symmetric. So, the statement is true.

Write each expression using exponents.11. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

12. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

13. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

14. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

15. 35

SOLUTION:  

16. 2 • 43

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

17. x2 – 6

SOLUTION:  

18. w3 + y2

SOLUTION:  

19. 2(y + z3)

SOLUTION:  

20. w4x

2yz

SOLUTION:  

21. TEETH Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

Write the prime factorization of each number. Use exponents for repeated factors.22. 34

SOLUTION:  34 = 2 • 17

23. 40

SOLUTION:  

24. 63

SOLUTION:  

25. 225

SOLUTION:  

Factor each monomial.26. 18x

SOLUTION:  18x = 2 • 3 • 3 • x

27. 10r2

SOLUTION:  

28. 32pq

SOLUTION:  32pq = 2 • 2 • 2 • 2 • 2 • p • q

29. –25ab2

SOLUTION:  

30. PHOTOGRAPHS Jacy has 24 photographs to put in a rectangular arrangement. In how many different numbers of rows and columns can she display them if each row has the same number of photographs? Name each arrangement.

SOLUTION:  List the different numbers of rows and columns by listing the factors of 24. So, Jacy could form rectangles with the following number of rows and columns: 1 • 24, 24 • 1, 2 • 12, 12 • 2, 3 • 8, 8 • 3, 4 • 6, 6 • 4. There are 8 different arrangements.

Find each product or quotient. Express using exponents.

31. 35 • 3

2

SOLUTION:  

32. (–7) • (–7)4

SOLUTION:  

33. m3 • m6

SOLUTION:  

34. x8 • x

SOLUTION:  

35. (2h7)(6h)

SOLUTION:  

36. (5a3)(–6a

4)

SOLUTION:  

37. 

SOLUTION:  

38. 

SOLUTION:  

39. PLANETS Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how

many times farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by thedistance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Write each expression using a positive exponent.

40. 9–4

SOLUTION:  

9–4

=

41. (–10)–2

SOLUTION:  

(–10)–2

=

42. m–5

SOLUTION:  

m–5 =

Write each fraction as an expression using a negative exponent other than –1.

43. 

SOLUTION:  

= 6–3

44. 

SOLUTION:  

or  or 

45. 

SOLUTION:  

46. MEASUREMENT If 1 millimeter is equal to 10–3

meter and 1 nanometer is equal to 10–9

meter, how many nanometers are in 1 millimeter? Write using a positive exponent.

SOLUTION:  To find the number of nanometers in 1 millimeter, divide the number of millimeters in a meter by the number of nanometers in a meter.

So, there are 106 nanometers in 1 millimeter.

Express each number in standard form.

47. 5.82 × 103

SOLUTION:  

48. 9.0 × 10–2

SOLUTION:  

49. 3.4 × 10–4

SOLUTION:  

50. 1.705 × 105

SOLUTION:  

Express each number in scientific notation.51. 379

SOLUTION:  

52. 26,880

SOLUTION:  

53. 0.0014

SOLUTION:  

54. 0.000561

SOLUTION:  

55. SPACE The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Simplify.

56. (26)3

SOLUTION:  

57. (r2)8

SOLUTION:  

58. (3x7)2

SOLUTION:  

59. (–2n4)6

SOLUTION:  

60. (4a9b)

4

SOLUTION:  

61. (5w5x

8)3

SOLUTION:  

62. GEOMETRY Find the area of the square shown below.

SOLUTION:  

Determine whether each graph, equation, or table represents a linear or nonlinear function. Explain.

63. 

SOLUTION:  The graph is a curve, not a straight line. So, it represents a nonlinear function.

64. 

SOLUTION:  The graph is a line. So, it represents a linear function.

65. y = x

SOLUTION:  

The equation y = x represents a linear function, because it is written in the form y = mx + b.

66. y =  + 1

SOLUTION:  

The equation y =  + 1 represents a nonlinear function, because it cannot be written in the form y = mx + b.

67. 

SOLUTION:  As x increases by 1, y decreases by 2. So, this is a linear function.

68. 

SOLUTION:  As x increases by 1, y increases by 10. So, this is a linear function.

69. SCHOOLS A school district’s spending on students over the last five years is represented by the equation y =

325x2 + 0.2x + 1427. Is this equation linear? Explain.

SOLUTION:  

The equation y = 325x2 + 0.2x + 1427 represents a nonlinear function, because it cannot be written in the form y =

mx + b.

Graph each function.

70. y = 3x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x2 (x, y)

–2 y = 3(–2)2 = 12 (–2, 12)

–1 y = 3(–1)2 = 3 (–1, 3)

0 y = 3(0)2 = 0 (0, 0)

1 y = 3(1)2 = 3 (1, 3)

2 y = 3(2)2 = 12 (2, 12)

71. y = –2x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –2x2 (x, y)

–2 y = –2(–2)2 = –8 (–2, –8)

–1 y = –2(–1)2 = –2 (–1, –2)

0 y = –2(0)2 = 0 (0, 0)

1 y = –2(1)2 = –2 (1, –2)

2 y = –2(2)2 = –8 (2, –8)

72. y = x2 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x2 – 4 (x, y)

–2 y = (–2)2 – 4 = 0 (–2, 0)

–1 y = (–1)2 – 4 = –3 (–1, –3)

0 y = 02 – 4 = –4 (0, –4)

1 y = 12 – 4 = –3 (1, –3)

2 y = 22 – 4 = 0 (2, 0)

73. y = –x2 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –x2 + 1 (x, y)

–2 y = –(–2)2 + 1 = –3 (–2, –3)

–1 y = –(–1)2 + 1 = 0 (–1, 0)

0 y = –(0)2 + 1 = 1 (0, 1)

1 y = –(1)2 + 1 = 0 (1, 0)

2 y = –(2)2 + 1 = –3 (2, –3)

74. y = 2x2 + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x2 + 2 (x, y)

–2 y = 2(–2)2 + 2 = 10 (–2, 10)

–1 y = 2(–1)2 + 2 = 4 (–1, 4)

0 y = 2(0)2 + 2 = 2 (0, 2)

1 y = 2(1)2 + 2 = 4 (1, 4)

2 y = 2(2)2 + 2 = 10 (2, 10)

75. y = x2 – 3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x

2 – 3

(x, y)

–2 y = (–2)

2 – 3 = –1

(–2, –1)

–1 y = (–1)

2 – 3 = –2.5

(–1, –2.5)

0 y = (0)

2 – 3 = –3

(0, –3)

1 y = (1)

2 – 3 = –2.5

(1, –2.5)

2 y = (2)

2 – 3 = –1

(2, –1)

76. GEOMETRY The volume of a cylinder with a height of 8 inches can be found using the equation V = 8(3.14)r2

where r is the radius of the cylinder. Graph the equation.

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

r V = 8(3.14)r2 (r, V)

0 V = 8(3.14)(02) = 0 (0, 0)

1 V = 8(3.14)(12) = 25.12 (1, 25.12)

2 V = 8(3.14)(22) = 100.48 (2, 100.48)

3 V = 8(3.14)(32) = 226.08 (3, 226.08)

4 V = 8(3.14)(42) = 401.92 (4, 401.92)

Graph each function.

77. y = x3 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 + 1 (x, y)

–2 y = (–2)3 + 1 = –7 (–2, –7)

–1 y = (–1)3 + 1 = 0 (–1, 0)

0 y = 03 + 1 = 1 (0, 1)

1 y = 13 + 1 = 2 (1, 2)

2 y = 23 + 1 = 9 (2, 9)

78. y = –3x3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –3x3 (x, y)

–2 y = –3(–2)3 = 24 (–2, 24)

–1 y = –3(–1)3 = 3 (–1, 3)

0 y = –3(0)3 = 0 (0, 0)

1 y = –3(1)3 = –3 (1, –3)

2 y = –3(2)3 = –24 (2, –24)

79. y = x3 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 – 4 (x, y)

–2 y = (–2)3 – 4 = –12 (–2, –12)

–1 y = (–1)3 – 4 = –5 (–1, –5)

0 y = 03 – 4 = –4 (0, –4)

1 y = 13 – 4 = –3 (1, –3)

2 y = 23 – 4 = 4 (2, 4)

80. y = 2x + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x + 2 (x, y)

–2 y = 2–2

+ 2 = 2.25 (–2, 2.25)

–1 y = 2–1

+ 2 = 2.5 (–1, 2.5)

0 y = 20+ 2 = 3 (0, 3)

1 y = 21 + 2 = 4 (1, 4)

2 y = 22 + 2 = 6 (2, 6)

81. y = 3x

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x (x, y)

–2 y = 3

–2 =

(–2, )

–1 y = 3

–1 =

(–1, )

0 y = 30 = 1 (0, 1)

1 y = 31 = 3 (1, 3)

2 y = 32 = 9 (2, 9)

82. y = 2x – 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x – 1 (x, y)

–2 y = 2–2

– 1 = –0.75 (–2, –0.75)

–1 y = 2–1

– 1 = –0.5 (–1, –0.5)

0 y = 20 – 1 = 0 (0, 0)

1 y = 21 – 1 = 1 (1, 1)

2 y = 22 – 1 = 3 (2, 3)

83. LIFE SCIENCE Starting from a single bacterium in a dish, the number of bacteria after t cycles of reproduction is

2t. A bacterium reproduces every 30 minutes. If there are 1000 bacteria in a dish now, how many will there be in 1

hour?

SOLUTION:  

To find the number of bacteria will be in the dish in 1 hour, replace t with 2 in the expression 2t because there are 2

thirty minute cycles in 2 hour. Then, multiply the result by 1000 because there are 1000 bacteria in the dish now.

So, there will be 4000 bacteria in the dish in 1 hour.

eSolutions Manual - Powered by Cognero Page 8

Study Guide and Review

Determine whether each statement is true or false . If false , replace the underlined word or number to make a true statement.

1. The exponent of a number raised to the first power can be omitted.

SOLUTION:  An exponent tells how many times a number is used as a factor. So, the exponent of a number raised to the first power can be omitted. The statement is true.

2. A number is in scientific notation when it does not contain exponents.

SOLUTION:  A number that is expressed as a product of a factor and a power of 10 is written in scientific notation. So, the statement is false. A number is in standard form when it does not contain exponents.

3. In 57, the number 7 is the base.

SOLUTION:  

The number that is multiplied is called the base. So, the statement is false. In 57, the number 7 is the exponent.

4. The number 49 is an example of a(n) prime number.

SOLUTION:  A prime number is a whole number that has exactly two unique factors, 1 and itself. So, the statement is false. The number 49 is an example of a composite number.

5. The equation y = 5x + 2 is an example of a(n) exponential function.

SOLUTION:  

An exponential function is a function that can be described by an equation of the form y = ax + c, where a ≠ 0 and 

a ≠ 1. So, the statement is true.

6. The graph of a(n) cubic function is called a parabola.

SOLUTION:  The statement is false. The graph of a quadratic function is called a parabola.

7. To multiply powers with the same base, add the exponents.

SOLUTION:  The statement is true.

8. A(n) nonlinear function has a constant rate of change.

SOLUTION:  Nonlinear functions do not have constant rates of change. So, the statement is false. A linear function has a constant rate of change.

9. To simplify (n6)5, the first step is to add 6 and 5.

SOLUTION:  

To find the power of a power, multiply exponents. So, the statement is false. To simplify (n6)5, the first step is to

multiply 6 and 5.

10. The graph of a(n) quadratic function is symmetric.

SOLUTION:  The graph of a quadratic function is a parabola, which is symmetric. So, the statement is true.

Write each expression using exponents.11. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

12. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

13. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

14. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

15. 35

SOLUTION:  

16. 2 • 43

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

17. x2 – 6

SOLUTION:  

18. w3 + y2

SOLUTION:  

19. 2(y + z3)

SOLUTION:  

20. w4x

2yz

SOLUTION:  

21. TEETH Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

Write the prime factorization of each number. Use exponents for repeated factors.22. 34

SOLUTION:  34 = 2 • 17

23. 40

SOLUTION:  

24. 63

SOLUTION:  

25. 225

SOLUTION:  

Factor each monomial.26. 18x

SOLUTION:  18x = 2 • 3 • 3 • x

27. 10r2

SOLUTION:  

28. 32pq

SOLUTION:  32pq = 2 • 2 • 2 • 2 • 2 • p • q

29. –25ab2

SOLUTION:  

30. PHOTOGRAPHS Jacy has 24 photographs to put in a rectangular arrangement. In how many different numbers of rows and columns can she display them if each row has the same number of photographs? Name each arrangement.

SOLUTION:  List the different numbers of rows and columns by listing the factors of 24. So, Jacy could form rectangles with the following number of rows and columns: 1 • 24, 24 • 1, 2 • 12, 12 • 2, 3 • 8, 8 • 3, 4 • 6, 6 • 4. There are 8 different arrangements.

Find each product or quotient. Express using exponents.

31. 35 • 3

2

SOLUTION:  

32. (–7) • (–7)4

SOLUTION:  

33. m3 • m6

SOLUTION:  

34. x8 • x

SOLUTION:  

35. (2h7)(6h)

SOLUTION:  

36. (5a3)(–6a

4)

SOLUTION:  

37. 

SOLUTION:  

38. 

SOLUTION:  

39. PLANETS Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how

many times farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by thedistance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Write each expression using a positive exponent.

40. 9–4

SOLUTION:  

9–4

=

41. (–10)–2

SOLUTION:  

(–10)–2

=

42. m–5

SOLUTION:  

m–5 =

Write each fraction as an expression using a negative exponent other than –1.

43. 

SOLUTION:  

= 6–3

44. 

SOLUTION:  

or  or 

45. 

SOLUTION:  

46. MEASUREMENT If 1 millimeter is equal to 10–3

meter and 1 nanometer is equal to 10–9

meter, how many nanometers are in 1 millimeter? Write using a positive exponent.

SOLUTION:  To find the number of nanometers in 1 millimeter, divide the number of millimeters in a meter by the number of nanometers in a meter.

So, there are 106 nanometers in 1 millimeter.

Express each number in standard form.

47. 5.82 × 103

SOLUTION:  

48. 9.0 × 10–2

SOLUTION:  

49. 3.4 × 10–4

SOLUTION:  

50. 1.705 × 105

SOLUTION:  

Express each number in scientific notation.51. 379

SOLUTION:  

52. 26,880

SOLUTION:  

53. 0.0014

SOLUTION:  

54. 0.000561

SOLUTION:  

55. SPACE The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Simplify.

56. (26)3

SOLUTION:  

57. (r2)8

SOLUTION:  

58. (3x7)2

SOLUTION:  

59. (–2n4)6

SOLUTION:  

60. (4a9b)

4

SOLUTION:  

61. (5w5x

8)3

SOLUTION:  

62. GEOMETRY Find the area of the square shown below.

SOLUTION:  

Determine whether each graph, equation, or table represents a linear or nonlinear function. Explain.

63. 

SOLUTION:  The graph is a curve, not a straight line. So, it represents a nonlinear function.

64. 

SOLUTION:  The graph is a line. So, it represents a linear function.

65. y = x

SOLUTION:  

The equation y = x represents a linear function, because it is written in the form y = mx + b.

66. y =  + 1

SOLUTION:  

The equation y =  + 1 represents a nonlinear function, because it cannot be written in the form y = mx + b.

67. 

SOLUTION:  As x increases by 1, y decreases by 2. So, this is a linear function.

68. 

SOLUTION:  As x increases by 1, y increases by 10. So, this is a linear function.

69. SCHOOLS A school district’s spending on students over the last five years is represented by the equation y =

325x2 + 0.2x + 1427. Is this equation linear? Explain.

SOLUTION:  

The equation y = 325x2 + 0.2x + 1427 represents a nonlinear function, because it cannot be written in the form y =

mx + b.

Graph each function.

70. y = 3x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x2 (x, y)

–2 y = 3(–2)2 = 12 (–2, 12)

–1 y = 3(–1)2 = 3 (–1, 3)

0 y = 3(0)2 = 0 (0, 0)

1 y = 3(1)2 = 3 (1, 3)

2 y = 3(2)2 = 12 (2, 12)

71. y = –2x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –2x2 (x, y)

–2 y = –2(–2)2 = –8 (–2, –8)

–1 y = –2(–1)2 = –2 (–1, –2)

0 y = –2(0)2 = 0 (0, 0)

1 y = –2(1)2 = –2 (1, –2)

2 y = –2(2)2 = –8 (2, –8)

72. y = x2 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x2 – 4 (x, y)

–2 y = (–2)2 – 4 = 0 (–2, 0)

–1 y = (–1)2 – 4 = –3 (–1, –3)

0 y = 02 – 4 = –4 (0, –4)

1 y = 12 – 4 = –3 (1, –3)

2 y = 22 – 4 = 0 (2, 0)

73. y = –x2 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –x2 + 1 (x, y)

–2 y = –(–2)2 + 1 = –3 (–2, –3)

–1 y = –(–1)2 + 1 = 0 (–1, 0)

0 y = –(0)2 + 1 = 1 (0, 1)

1 y = –(1)2 + 1 = 0 (1, 0)

2 y = –(2)2 + 1 = –3 (2, –3)

74. y = 2x2 + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x2 + 2 (x, y)

–2 y = 2(–2)2 + 2 = 10 (–2, 10)

–1 y = 2(–1)2 + 2 = 4 (–1, 4)

0 y = 2(0)2 + 2 = 2 (0, 2)

1 y = 2(1)2 + 2 = 4 (1, 4)

2 y = 2(2)2 + 2 = 10 (2, 10)

75. y = x2 – 3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x

2 – 3

(x, y)

–2 y = (–2)

2 – 3 = –1

(–2, –1)

–1 y = (–1)

2 – 3 = –2.5

(–1, –2.5)

0 y = (0)

2 – 3 = –3

(0, –3)

1 y = (1)

2 – 3 = –2.5

(1, –2.5)

2 y = (2)

2 – 3 = –1

(2, –1)

76. GEOMETRY The volume of a cylinder with a height of 8 inches can be found using the equation V = 8(3.14)r2

where r is the radius of the cylinder. Graph the equation.

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

r V = 8(3.14)r2 (r, V)

0 V = 8(3.14)(02) = 0 (0, 0)

1 V = 8(3.14)(12) = 25.12 (1, 25.12)

2 V = 8(3.14)(22) = 100.48 (2, 100.48)

3 V = 8(3.14)(32) = 226.08 (3, 226.08)

4 V = 8(3.14)(42) = 401.92 (4, 401.92)

Graph each function.

77. y = x3 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 + 1 (x, y)

–2 y = (–2)3 + 1 = –7 (–2, –7)

–1 y = (–1)3 + 1 = 0 (–1, 0)

0 y = 03 + 1 = 1 (0, 1)

1 y = 13 + 1 = 2 (1, 2)

2 y = 23 + 1 = 9 (2, 9)

78. y = –3x3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –3x3 (x, y)

–2 y = –3(–2)3 = 24 (–2, 24)

–1 y = –3(–1)3 = 3 (–1, 3)

0 y = –3(0)3 = 0 (0, 0)

1 y = –3(1)3 = –3 (1, –3)

2 y = –3(2)3 = –24 (2, –24)

79. y = x3 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 – 4 (x, y)

–2 y = (–2)3 – 4 = –12 (–2, –12)

–1 y = (–1)3 – 4 = –5 (–1, –5)

0 y = 03 – 4 = –4 (0, –4)

1 y = 13 – 4 = –3 (1, –3)

2 y = 23 – 4 = 4 (2, 4)

80. y = 2x + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x + 2 (x, y)

–2 y = 2–2

+ 2 = 2.25 (–2, 2.25)

–1 y = 2–1

+ 2 = 2.5 (–1, 2.5)

0 y = 20+ 2 = 3 (0, 3)

1 y = 21 + 2 = 4 (1, 4)

2 y = 22 + 2 = 6 (2, 6)

81. y = 3x

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x (x, y)

–2 y = 3

–2 =

(–2, )

–1 y = 3

–1 =

(–1, )

0 y = 30 = 1 (0, 1)

1 y = 31 = 3 (1, 3)

2 y = 32 = 9 (2, 9)

82. y = 2x – 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x – 1 (x, y)

–2 y = 2–2

– 1 = –0.75 (–2, –0.75)

–1 y = 2–1

– 1 = –0.5 (–1, –0.5)

0 y = 20 – 1 = 0 (0, 0)

1 y = 21 – 1 = 1 (1, 1)

2 y = 22 – 1 = 3 (2, 3)

83. LIFE SCIENCE Starting from a single bacterium in a dish, the number of bacteria after t cycles of reproduction is

2t. A bacterium reproduces every 30 minutes. If there are 1000 bacteria in a dish now, how many will there be in 1

hour?

SOLUTION:  

To find the number of bacteria will be in the dish in 1 hour, replace t with 2 in the expression 2t because there are 2

thirty minute cycles in 2 hour. Then, multiply the result by 1000 because there are 1000 bacteria in the dish now.

So, there will be 4000 bacteria in the dish in 1 hour.

eSolutions Manual - Powered by Cognero Page 9

Study Guide and Review

Determine whether each statement is true or false . If false , replace the underlined word or number to make a true statement.

1. The exponent of a number raised to the first power can be omitted.

SOLUTION:  An exponent tells how many times a number is used as a factor. So, the exponent of a number raised to the first power can be omitted. The statement is true.

2. A number is in scientific notation when it does not contain exponents.

SOLUTION:  A number that is expressed as a product of a factor and a power of 10 is written in scientific notation. So, the statement is false. A number is in standard form when it does not contain exponents.

3. In 57, the number 7 is the base.

SOLUTION:  

The number that is multiplied is called the base. So, the statement is false. In 57, the number 7 is the exponent.

4. The number 49 is an example of a(n) prime number.

SOLUTION:  A prime number is a whole number that has exactly two unique factors, 1 and itself. So, the statement is false. The number 49 is an example of a composite number.

5. The equation y = 5x + 2 is an example of a(n) exponential function.

SOLUTION:  

An exponential function is a function that can be described by an equation of the form y = ax + c, where a ≠ 0 and 

a ≠ 1. So, the statement is true.

6. The graph of a(n) cubic function is called a parabola.

SOLUTION:  The statement is false. The graph of a quadratic function is called a parabola.

7. To multiply powers with the same base, add the exponents.

SOLUTION:  The statement is true.

8. A(n) nonlinear function has a constant rate of change.

SOLUTION:  Nonlinear functions do not have constant rates of change. So, the statement is false. A linear function has a constant rate of change.

9. To simplify (n6)5, the first step is to add 6 and 5.

SOLUTION:  

To find the power of a power, multiply exponents. So, the statement is false. To simplify (n6)5, the first step is to

multiply 6 and 5.

10. The graph of a(n) quadratic function is symmetric.

SOLUTION:  The graph of a quadratic function is a parabola, which is symmetric. So, the statement is true.

Write each expression using exponents.11. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

12. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

13. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

14. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

15. 35

SOLUTION:  

16. 2 • 43

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

17. x2 – 6

SOLUTION:  

18. w3 + y2

SOLUTION:  

19. 2(y + z3)

SOLUTION:  

20. w4x

2yz

SOLUTION:  

21. TEETH Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

Write the prime factorization of each number. Use exponents for repeated factors.22. 34

SOLUTION:  34 = 2 • 17

23. 40

SOLUTION:  

24. 63

SOLUTION:  

25. 225

SOLUTION:  

Factor each monomial.26. 18x

SOLUTION:  18x = 2 • 3 • 3 • x

27. 10r2

SOLUTION:  

28. 32pq

SOLUTION:  32pq = 2 • 2 • 2 • 2 • 2 • p • q

29. –25ab2

SOLUTION:  

30. PHOTOGRAPHS Jacy has 24 photographs to put in a rectangular arrangement. In how many different numbers of rows and columns can she display them if each row has the same number of photographs? Name each arrangement.

SOLUTION:  List the different numbers of rows and columns by listing the factors of 24. So, Jacy could form rectangles with the following number of rows and columns: 1 • 24, 24 • 1, 2 • 12, 12 • 2, 3 • 8, 8 • 3, 4 • 6, 6 • 4. There are 8 different arrangements.

Find each product or quotient. Express using exponents.

31. 35 • 3

2

SOLUTION:  

32. (–7) • (–7)4

SOLUTION:  

33. m3 • m6

SOLUTION:  

34. x8 • x

SOLUTION:  

35. (2h7)(6h)

SOLUTION:  

36. (5a3)(–6a

4)

SOLUTION:  

37. 

SOLUTION:  

38. 

SOLUTION:  

39. PLANETS Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how

many times farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by thedistance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Write each expression using a positive exponent.

40. 9–4

SOLUTION:  

9–4

=

41. (–10)–2

SOLUTION:  

(–10)–2

=

42. m–5

SOLUTION:  

m–5 =

Write each fraction as an expression using a negative exponent other than –1.

43. 

SOLUTION:  

= 6–3

44. 

SOLUTION:  

or  or 

45. 

SOLUTION:  

46. MEASUREMENT If 1 millimeter is equal to 10–3

meter and 1 nanometer is equal to 10–9

meter, how many nanometers are in 1 millimeter? Write using a positive exponent.

SOLUTION:  To find the number of nanometers in 1 millimeter, divide the number of millimeters in a meter by the number of nanometers in a meter.

So, there are 106 nanometers in 1 millimeter.

Express each number in standard form.

47. 5.82 × 103

SOLUTION:  

48. 9.0 × 10–2

SOLUTION:  

49. 3.4 × 10–4

SOLUTION:  

50. 1.705 × 105

SOLUTION:  

Express each number in scientific notation.51. 379

SOLUTION:  

52. 26,880

SOLUTION:  

53. 0.0014

SOLUTION:  

54. 0.000561

SOLUTION:  

55. SPACE The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Simplify.

56. (26)3

SOLUTION:  

57. (r2)8

SOLUTION:  

58. (3x7)2

SOLUTION:  

59. (–2n4)6

SOLUTION:  

60. (4a9b)

4

SOLUTION:  

61. (5w5x

8)3

SOLUTION:  

62. GEOMETRY Find the area of the square shown below.

SOLUTION:  

Determine whether each graph, equation, or table represents a linear or nonlinear function. Explain.

63. 

SOLUTION:  The graph is a curve, not a straight line. So, it represents a nonlinear function.

64. 

SOLUTION:  The graph is a line. So, it represents a linear function.

65. y = x

SOLUTION:  

The equation y = x represents a linear function, because it is written in the form y = mx + b.

66. y =  + 1

SOLUTION:  

The equation y =  + 1 represents a nonlinear function, because it cannot be written in the form y = mx + b.

67. 

SOLUTION:  As x increases by 1, y decreases by 2. So, this is a linear function.

68. 

SOLUTION:  As x increases by 1, y increases by 10. So, this is a linear function.

69. SCHOOLS A school district’s spending on students over the last five years is represented by the equation y =

325x2 + 0.2x + 1427. Is this equation linear? Explain.

SOLUTION:  

The equation y = 325x2 + 0.2x + 1427 represents a nonlinear function, because it cannot be written in the form y =

mx + b.

Graph each function.

70. y = 3x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x2 (x, y)

–2 y = 3(–2)2 = 12 (–2, 12)

–1 y = 3(–1)2 = 3 (–1, 3)

0 y = 3(0)2 = 0 (0, 0)

1 y = 3(1)2 = 3 (1, 3)

2 y = 3(2)2 = 12 (2, 12)

71. y = –2x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –2x2 (x, y)

–2 y = –2(–2)2 = –8 (–2, –8)

–1 y = –2(–1)2 = –2 (–1, –2)

0 y = –2(0)2 = 0 (0, 0)

1 y = –2(1)2 = –2 (1, –2)

2 y = –2(2)2 = –8 (2, –8)

72. y = x2 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x2 – 4 (x, y)

–2 y = (–2)2 – 4 = 0 (–2, 0)

–1 y = (–1)2 – 4 = –3 (–1, –3)

0 y = 02 – 4 = –4 (0, –4)

1 y = 12 – 4 = –3 (1, –3)

2 y = 22 – 4 = 0 (2, 0)

73. y = –x2 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –x2 + 1 (x, y)

–2 y = –(–2)2 + 1 = –3 (–2, –3)

–1 y = –(–1)2 + 1 = 0 (–1, 0)

0 y = –(0)2 + 1 = 1 (0, 1)

1 y = –(1)2 + 1 = 0 (1, 0)

2 y = –(2)2 + 1 = –3 (2, –3)

74. y = 2x2 + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x2 + 2 (x, y)

–2 y = 2(–2)2 + 2 = 10 (–2, 10)

–1 y = 2(–1)2 + 2 = 4 (–1, 4)

0 y = 2(0)2 + 2 = 2 (0, 2)

1 y = 2(1)2 + 2 = 4 (1, 4)

2 y = 2(2)2 + 2 = 10 (2, 10)

75. y = x2 – 3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x

2 – 3

(x, y)

–2 y = (–2)

2 – 3 = –1

(–2, –1)

–1 y = (–1)

2 – 3 = –2.5

(–1, –2.5)

0 y = (0)

2 – 3 = –3

(0, –3)

1 y = (1)

2 – 3 = –2.5

(1, –2.5)

2 y = (2)

2 – 3 = –1

(2, –1)

76. GEOMETRY The volume of a cylinder with a height of 8 inches can be found using the equation V = 8(3.14)r2

where r is the radius of the cylinder. Graph the equation.

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

r V = 8(3.14)r2 (r, V)

0 V = 8(3.14)(02) = 0 (0, 0)

1 V = 8(3.14)(12) = 25.12 (1, 25.12)

2 V = 8(3.14)(22) = 100.48 (2, 100.48)

3 V = 8(3.14)(32) = 226.08 (3, 226.08)

4 V = 8(3.14)(42) = 401.92 (4, 401.92)

Graph each function.

77. y = x3 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 + 1 (x, y)

–2 y = (–2)3 + 1 = –7 (–2, –7)

–1 y = (–1)3 + 1 = 0 (–1, 0)

0 y = 03 + 1 = 1 (0, 1)

1 y = 13 + 1 = 2 (1, 2)

2 y = 23 + 1 = 9 (2, 9)

78. y = –3x3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –3x3 (x, y)

–2 y = –3(–2)3 = 24 (–2, 24)

–1 y = –3(–1)3 = 3 (–1, 3)

0 y = –3(0)3 = 0 (0, 0)

1 y = –3(1)3 = –3 (1, –3)

2 y = –3(2)3 = –24 (2, –24)

79. y = x3 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 – 4 (x, y)

–2 y = (–2)3 – 4 = –12 (–2, –12)

–1 y = (–1)3 – 4 = –5 (–1, –5)

0 y = 03 – 4 = –4 (0, –4)

1 y = 13 – 4 = –3 (1, –3)

2 y = 23 – 4 = 4 (2, 4)

80. y = 2x + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x + 2 (x, y)

–2 y = 2–2

+ 2 = 2.25 (–2, 2.25)

–1 y = 2–1

+ 2 = 2.5 (–1, 2.5)

0 y = 20+ 2 = 3 (0, 3)

1 y = 21 + 2 = 4 (1, 4)

2 y = 22 + 2 = 6 (2, 6)

81. y = 3x

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x (x, y)

–2 y = 3

–2 =

(–2, )

–1 y = 3

–1 =

(–1, )

0 y = 30 = 1 (0, 1)

1 y = 31 = 3 (1, 3)

2 y = 32 = 9 (2, 9)

82. y = 2x – 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x – 1 (x, y)

–2 y = 2–2

– 1 = –0.75 (–2, –0.75)

–1 y = 2–1

– 1 = –0.5 (–1, –0.5)

0 y = 20 – 1 = 0 (0, 0)

1 y = 21 – 1 = 1 (1, 1)

2 y = 22 – 1 = 3 (2, 3)

83. LIFE SCIENCE Starting from a single bacterium in a dish, the number of bacteria after t cycles of reproduction is

2t. A bacterium reproduces every 30 minutes. If there are 1000 bacteria in a dish now, how many will there be in 1

hour?

SOLUTION:  

To find the number of bacteria will be in the dish in 1 hour, replace t with 2 in the expression 2t because there are 2

thirty minute cycles in 2 hour. Then, multiply the result by 1000 because there are 1000 bacteria in the dish now.

So, there will be 4000 bacteria in the dish in 1 hour.

eSolutions Manual - Powered by Cognero Page 10

Study Guide and Review

Determine whether each statement is true or false . If false , replace the underlined word or number to make a true statement.

1. The exponent of a number raised to the first power can be omitted.

SOLUTION:  An exponent tells how many times a number is used as a factor. So, the exponent of a number raised to the first power can be omitted. The statement is true.

2. A number is in scientific notation when it does not contain exponents.

SOLUTION:  A number that is expressed as a product of a factor and a power of 10 is written in scientific notation. So, the statement is false. A number is in standard form when it does not contain exponents.

3. In 57, the number 7 is the base.

SOLUTION:  

The number that is multiplied is called the base. So, the statement is false. In 57, the number 7 is the exponent.

4. The number 49 is an example of a(n) prime number.

SOLUTION:  A prime number is a whole number that has exactly two unique factors, 1 and itself. So, the statement is false. The number 49 is an example of a composite number.

5. The equation y = 5x + 2 is an example of a(n) exponential function.

SOLUTION:  

An exponential function is a function that can be described by an equation of the form y = ax + c, where a ≠ 0 and 

a ≠ 1. So, the statement is true.

6. The graph of a(n) cubic function is called a parabola.

SOLUTION:  The statement is false. The graph of a quadratic function is called a parabola.

7. To multiply powers with the same base, add the exponents.

SOLUTION:  The statement is true.

8. A(n) nonlinear function has a constant rate of change.

SOLUTION:  Nonlinear functions do not have constant rates of change. So, the statement is false. A linear function has a constant rate of change.

9. To simplify (n6)5, the first step is to add 6 and 5.

SOLUTION:  

To find the power of a power, multiply exponents. So, the statement is false. To simplify (n6)5, the first step is to

multiply 6 and 5.

10. The graph of a(n) quadratic function is symmetric.

SOLUTION:  The graph of a quadratic function is a parabola, which is symmetric. So, the statement is true.

Write each expression using exponents.11. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

12. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

13. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

14. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

15. 35

SOLUTION:  

16. 2 • 43

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

17. x2 – 6

SOLUTION:  

18. w3 + y2

SOLUTION:  

19. 2(y + z3)

SOLUTION:  

20. w4x

2yz

SOLUTION:  

21. TEETH Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

Write the prime factorization of each number. Use exponents for repeated factors.22. 34

SOLUTION:  34 = 2 • 17

23. 40

SOLUTION:  

24. 63

SOLUTION:  

25. 225

SOLUTION:  

Factor each monomial.26. 18x

SOLUTION:  18x = 2 • 3 • 3 • x

27. 10r2

SOLUTION:  

28. 32pq

SOLUTION:  32pq = 2 • 2 • 2 • 2 • 2 • p • q

29. –25ab2

SOLUTION:  

30. PHOTOGRAPHS Jacy has 24 photographs to put in a rectangular arrangement. In how many different numbers of rows and columns can she display them if each row has the same number of photographs? Name each arrangement.

SOLUTION:  List the different numbers of rows and columns by listing the factors of 24. So, Jacy could form rectangles with the following number of rows and columns: 1 • 24, 24 • 1, 2 • 12, 12 • 2, 3 • 8, 8 • 3, 4 • 6, 6 • 4. There are 8 different arrangements.

Find each product or quotient. Express using exponents.

31. 35 • 3

2

SOLUTION:  

32. (–7) • (–7)4

SOLUTION:  

33. m3 • m6

SOLUTION:  

34. x8 • x

SOLUTION:  

35. (2h7)(6h)

SOLUTION:  

36. (5a3)(–6a

4)

SOLUTION:  

37. 

SOLUTION:  

38. 

SOLUTION:  

39. PLANETS Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how

many times farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by thedistance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Write each expression using a positive exponent.

40. 9–4

SOLUTION:  

9–4

=

41. (–10)–2

SOLUTION:  

(–10)–2

=

42. m–5

SOLUTION:  

m–5 =

Write each fraction as an expression using a negative exponent other than –1.

43. 

SOLUTION:  

= 6–3

44. 

SOLUTION:  

or  or 

45. 

SOLUTION:  

46. MEASUREMENT If 1 millimeter is equal to 10–3

meter and 1 nanometer is equal to 10–9

meter, how many nanometers are in 1 millimeter? Write using a positive exponent.

SOLUTION:  To find the number of nanometers in 1 millimeter, divide the number of millimeters in a meter by the number of nanometers in a meter.

So, there are 106 nanometers in 1 millimeter.

Express each number in standard form.

47. 5.82 × 103

SOLUTION:  

48. 9.0 × 10–2

SOLUTION:  

49. 3.4 × 10–4

SOLUTION:  

50. 1.705 × 105

SOLUTION:  

Express each number in scientific notation.51. 379

SOLUTION:  

52. 26,880

SOLUTION:  

53. 0.0014

SOLUTION:  

54. 0.000561

SOLUTION:  

55. SPACE The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Simplify.

56. (26)3

SOLUTION:  

57. (r2)8

SOLUTION:  

58. (3x7)2

SOLUTION:  

59. (–2n4)6

SOLUTION:  

60. (4a9b)

4

SOLUTION:  

61. (5w5x

8)3

SOLUTION:  

62. GEOMETRY Find the area of the square shown below.

SOLUTION:  

Determine whether each graph, equation, or table represents a linear or nonlinear function. Explain.

63. 

SOLUTION:  The graph is a curve, not a straight line. So, it represents a nonlinear function.

64. 

SOLUTION:  The graph is a line. So, it represents a linear function.

65. y = x

SOLUTION:  

The equation y = x represents a linear function, because it is written in the form y = mx + b.

66. y =  + 1

SOLUTION:  

The equation y =  + 1 represents a nonlinear function, because it cannot be written in the form y = mx + b.

67. 

SOLUTION:  As x increases by 1, y decreases by 2. So, this is a linear function.

68. 

SOLUTION:  As x increases by 1, y increases by 10. So, this is a linear function.

69. SCHOOLS A school district’s spending on students over the last five years is represented by the equation y =

325x2 + 0.2x + 1427. Is this equation linear? Explain.

SOLUTION:  

The equation y = 325x2 + 0.2x + 1427 represents a nonlinear function, because it cannot be written in the form y =

mx + b.

Graph each function.

70. y = 3x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x2 (x, y)

–2 y = 3(–2)2 = 12 (–2, 12)

–1 y = 3(–1)2 = 3 (–1, 3)

0 y = 3(0)2 = 0 (0, 0)

1 y = 3(1)2 = 3 (1, 3)

2 y = 3(2)2 = 12 (2, 12)

71. y = –2x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –2x2 (x, y)

–2 y = –2(–2)2 = –8 (–2, –8)

–1 y = –2(–1)2 = –2 (–1, –2)

0 y = –2(0)2 = 0 (0, 0)

1 y = –2(1)2 = –2 (1, –2)

2 y = –2(2)2 = –8 (2, –8)

72. y = x2 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x2 – 4 (x, y)

–2 y = (–2)2 – 4 = 0 (–2, 0)

–1 y = (–1)2 – 4 = –3 (–1, –3)

0 y = 02 – 4 = –4 (0, –4)

1 y = 12 – 4 = –3 (1, –3)

2 y = 22 – 4 = 0 (2, 0)

73. y = –x2 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –x2 + 1 (x, y)

–2 y = –(–2)2 + 1 = –3 (–2, –3)

–1 y = –(–1)2 + 1 = 0 (–1, 0)

0 y = –(0)2 + 1 = 1 (0, 1)

1 y = –(1)2 + 1 = 0 (1, 0)

2 y = –(2)2 + 1 = –3 (2, –3)

74. y = 2x2 + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x2 + 2 (x, y)

–2 y = 2(–2)2 + 2 = 10 (–2, 10)

–1 y = 2(–1)2 + 2 = 4 (–1, 4)

0 y = 2(0)2 + 2 = 2 (0, 2)

1 y = 2(1)2 + 2 = 4 (1, 4)

2 y = 2(2)2 + 2 = 10 (2, 10)

75. y = x2 – 3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x

2 – 3

(x, y)

–2 y = (–2)

2 – 3 = –1

(–2, –1)

–1 y = (–1)

2 – 3 = –2.5

(–1, –2.5)

0 y = (0)

2 – 3 = –3

(0, –3)

1 y = (1)

2 – 3 = –2.5

(1, –2.5)

2 y = (2)

2 – 3 = –1

(2, –1)

76. GEOMETRY The volume of a cylinder with a height of 8 inches can be found using the equation V = 8(3.14)r2

where r is the radius of the cylinder. Graph the equation.

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

r V = 8(3.14)r2 (r, V)

0 V = 8(3.14)(02) = 0 (0, 0)

1 V = 8(3.14)(12) = 25.12 (1, 25.12)

2 V = 8(3.14)(22) = 100.48 (2, 100.48)

3 V = 8(3.14)(32) = 226.08 (3, 226.08)

4 V = 8(3.14)(42) = 401.92 (4, 401.92)

Graph each function.

77. y = x3 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 + 1 (x, y)

–2 y = (–2)3 + 1 = –7 (–2, –7)

–1 y = (–1)3 + 1 = 0 (–1, 0)

0 y = 03 + 1 = 1 (0, 1)

1 y = 13 + 1 = 2 (1, 2)

2 y = 23 + 1 = 9 (2, 9)

78. y = –3x3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –3x3 (x, y)

–2 y = –3(–2)3 = 24 (–2, 24)

–1 y = –3(–1)3 = 3 (–1, 3)

0 y = –3(0)3 = 0 (0, 0)

1 y = –3(1)3 = –3 (1, –3)

2 y = –3(2)3 = –24 (2, –24)

79. y = x3 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 – 4 (x, y)

–2 y = (–2)3 – 4 = –12 (–2, –12)

–1 y = (–1)3 – 4 = –5 (–1, –5)

0 y = 03 – 4 = –4 (0, –4)

1 y = 13 – 4 = –3 (1, –3)

2 y = 23 – 4 = 4 (2, 4)

80. y = 2x + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x + 2 (x, y)

–2 y = 2–2

+ 2 = 2.25 (–2, 2.25)

–1 y = 2–1

+ 2 = 2.5 (–1, 2.5)

0 y = 20+ 2 = 3 (0, 3)

1 y = 21 + 2 = 4 (1, 4)

2 y = 22 + 2 = 6 (2, 6)

81. y = 3x

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x (x, y)

–2 y = 3

–2 =

(–2, )

–1 y = 3

–1 =

(–1, )

0 y = 30 = 1 (0, 1)

1 y = 31 = 3 (1, 3)

2 y = 32 = 9 (2, 9)

82. y = 2x – 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x – 1 (x, y)

–2 y = 2–2

– 1 = –0.75 (–2, –0.75)

–1 y = 2–1

– 1 = –0.5 (–1, –0.5)

0 y = 20 – 1 = 0 (0, 0)

1 y = 21 – 1 = 1 (1, 1)

2 y = 22 – 1 = 3 (2, 3)

83. LIFE SCIENCE Starting from a single bacterium in a dish, the number of bacteria after t cycles of reproduction is

2t. A bacterium reproduces every 30 minutes. If there are 1000 bacteria in a dish now, how many will there be in 1

hour?

SOLUTION:  

To find the number of bacteria will be in the dish in 1 hour, replace t with 2 in the expression 2t because there are 2

thirty minute cycles in 2 hour. Then, multiply the result by 1000 because there are 1000 bacteria in the dish now.

So, there will be 4000 bacteria in the dish in 1 hour.

eSolutions Manual - Powered by Cognero Page 11

Study Guide and Review

Determine whether each statement is true or false . If false , replace the underlined word or number to make a true statement.

1. The exponent of a number raised to the first power can be omitted.

SOLUTION:  An exponent tells how many times a number is used as a factor. So, the exponent of a number raised to the first power can be omitted. The statement is true.

2. A number is in scientific notation when it does not contain exponents.

SOLUTION:  A number that is expressed as a product of a factor and a power of 10 is written in scientific notation. So, the statement is false. A number is in standard form when it does not contain exponents.

3. In 57, the number 7 is the base.

SOLUTION:  

The number that is multiplied is called the base. So, the statement is false. In 57, the number 7 is the exponent.

4. The number 49 is an example of a(n) prime number.

SOLUTION:  A prime number is a whole number that has exactly two unique factors, 1 and itself. So, the statement is false. The number 49 is an example of a composite number.

5. The equation y = 5x + 2 is an example of a(n) exponential function.

SOLUTION:  

An exponential function is a function that can be described by an equation of the form y = ax + c, where a ≠ 0 and 

a ≠ 1. So, the statement is true.

6. The graph of a(n) cubic function is called a parabola.

SOLUTION:  The statement is false. The graph of a quadratic function is called a parabola.

7. To multiply powers with the same base, add the exponents.

SOLUTION:  The statement is true.

8. A(n) nonlinear function has a constant rate of change.

SOLUTION:  Nonlinear functions do not have constant rates of change. So, the statement is false. A linear function has a constant rate of change.

9. To simplify (n6)5, the first step is to add 6 and 5.

SOLUTION:  

To find the power of a power, multiply exponents. So, the statement is false. To simplify (n6)5, the first step is to

multiply 6 and 5.

10. The graph of a(n) quadratic function is symmetric.

SOLUTION:  The graph of a quadratic function is a parabola, which is symmetric. So, the statement is true.

Write each expression using exponents.11. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

12. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

13. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

14. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

15. 35

SOLUTION:  

16. 2 • 43

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

17. x2 – 6

SOLUTION:  

18. w3 + y2

SOLUTION:  

19. 2(y + z3)

SOLUTION:  

20. w4x

2yz

SOLUTION:  

21. TEETH Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

Write the prime factorization of each number. Use exponents for repeated factors.22. 34

SOLUTION:  34 = 2 • 17

23. 40

SOLUTION:  

24. 63

SOLUTION:  

25. 225

SOLUTION:  

Factor each monomial.26. 18x

SOLUTION:  18x = 2 • 3 • 3 • x

27. 10r2

SOLUTION:  

28. 32pq

SOLUTION:  32pq = 2 • 2 • 2 • 2 • 2 • p • q

29. –25ab2

SOLUTION:  

30. PHOTOGRAPHS Jacy has 24 photographs to put in a rectangular arrangement. In how many different numbers of rows and columns can she display them if each row has the same number of photographs? Name each arrangement.

SOLUTION:  List the different numbers of rows and columns by listing the factors of 24. So, Jacy could form rectangles with the following number of rows and columns: 1 • 24, 24 • 1, 2 • 12, 12 • 2, 3 • 8, 8 • 3, 4 • 6, 6 • 4. There are 8 different arrangements.

Find each product or quotient. Express using exponents.

31. 35 • 3

2

SOLUTION:  

32. (–7) • (–7)4

SOLUTION:  

33. m3 • m6

SOLUTION:  

34. x8 • x

SOLUTION:  

35. (2h7)(6h)

SOLUTION:  

36. (5a3)(–6a

4)

SOLUTION:  

37. 

SOLUTION:  

38. 

SOLUTION:  

39. PLANETS Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how

many times farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by thedistance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Write each expression using a positive exponent.

40. 9–4

SOLUTION:  

9–4

=

41. (–10)–2

SOLUTION:  

(–10)–2

=

42. m–5

SOLUTION:  

m–5 =

Write each fraction as an expression using a negative exponent other than –1.

43. 

SOLUTION:  

= 6–3

44. 

SOLUTION:  

or  or 

45. 

SOLUTION:  

46. MEASUREMENT If 1 millimeter is equal to 10–3

meter and 1 nanometer is equal to 10–9

meter, how many nanometers are in 1 millimeter? Write using a positive exponent.

SOLUTION:  To find the number of nanometers in 1 millimeter, divide the number of millimeters in a meter by the number of nanometers in a meter.

So, there are 106 nanometers in 1 millimeter.

Express each number in standard form.

47. 5.82 × 103

SOLUTION:  

48. 9.0 × 10–2

SOLUTION:  

49. 3.4 × 10–4

SOLUTION:  

50. 1.705 × 105

SOLUTION:  

Express each number in scientific notation.51. 379

SOLUTION:  

52. 26,880

SOLUTION:  

53. 0.0014

SOLUTION:  

54. 0.000561

SOLUTION:  

55. SPACE The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Simplify.

56. (26)3

SOLUTION:  

57. (r2)8

SOLUTION:  

58. (3x7)2

SOLUTION:  

59. (–2n4)6

SOLUTION:  

60. (4a9b)

4

SOLUTION:  

61. (5w5x

8)3

SOLUTION:  

62. GEOMETRY Find the area of the square shown below.

SOLUTION:  

Determine whether each graph, equation, or table represents a linear or nonlinear function. Explain.

63. 

SOLUTION:  The graph is a curve, not a straight line. So, it represents a nonlinear function.

64. 

SOLUTION:  The graph is a line. So, it represents a linear function.

65. y = x

SOLUTION:  

The equation y = x represents a linear function, because it is written in the form y = mx + b.

66. y =  + 1

SOLUTION:  

The equation y =  + 1 represents a nonlinear function, because it cannot be written in the form y = mx + b.

67. 

SOLUTION:  As x increases by 1, y decreases by 2. So, this is a linear function.

68. 

SOLUTION:  As x increases by 1, y increases by 10. So, this is a linear function.

69. SCHOOLS A school district’s spending on students over the last five years is represented by the equation y =

325x2 + 0.2x + 1427. Is this equation linear? Explain.

SOLUTION:  

The equation y = 325x2 + 0.2x + 1427 represents a nonlinear function, because it cannot be written in the form y =

mx + b.

Graph each function.

70. y = 3x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x2 (x, y)

–2 y = 3(–2)2 = 12 (–2, 12)

–1 y = 3(–1)2 = 3 (–1, 3)

0 y = 3(0)2 = 0 (0, 0)

1 y = 3(1)2 = 3 (1, 3)

2 y = 3(2)2 = 12 (2, 12)

71. y = –2x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –2x2 (x, y)

–2 y = –2(–2)2 = –8 (–2, –8)

–1 y = –2(–1)2 = –2 (–1, –2)

0 y = –2(0)2 = 0 (0, 0)

1 y = –2(1)2 = –2 (1, –2)

2 y = –2(2)2 = –8 (2, –8)

72. y = x2 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x2 – 4 (x, y)

–2 y = (–2)2 – 4 = 0 (–2, 0)

–1 y = (–1)2 – 4 = –3 (–1, –3)

0 y = 02 – 4 = –4 (0, –4)

1 y = 12 – 4 = –3 (1, –3)

2 y = 22 – 4 = 0 (2, 0)

73. y = –x2 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –x2 + 1 (x, y)

–2 y = –(–2)2 + 1 = –3 (–2, –3)

–1 y = –(–1)2 + 1 = 0 (–1, 0)

0 y = –(0)2 + 1 = 1 (0, 1)

1 y = –(1)2 + 1 = 0 (1, 0)

2 y = –(2)2 + 1 = –3 (2, –3)

74. y = 2x2 + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x2 + 2 (x, y)

–2 y = 2(–2)2 + 2 = 10 (–2, 10)

–1 y = 2(–1)2 + 2 = 4 (–1, 4)

0 y = 2(0)2 + 2 = 2 (0, 2)

1 y = 2(1)2 + 2 = 4 (1, 4)

2 y = 2(2)2 + 2 = 10 (2, 10)

75. y = x2 – 3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x

2 – 3

(x, y)

–2 y = (–2)

2 – 3 = –1

(–2, –1)

–1 y = (–1)

2 – 3 = –2.5

(–1, –2.5)

0 y = (0)

2 – 3 = –3

(0, –3)

1 y = (1)

2 – 3 = –2.5

(1, –2.5)

2 y = (2)

2 – 3 = –1

(2, –1)

76. GEOMETRY The volume of a cylinder with a height of 8 inches can be found using the equation V = 8(3.14)r2

where r is the radius of the cylinder. Graph the equation.

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

r V = 8(3.14)r2 (r, V)

0 V = 8(3.14)(02) = 0 (0, 0)

1 V = 8(3.14)(12) = 25.12 (1, 25.12)

2 V = 8(3.14)(22) = 100.48 (2, 100.48)

3 V = 8(3.14)(32) = 226.08 (3, 226.08)

4 V = 8(3.14)(42) = 401.92 (4, 401.92)

Graph each function.

77. y = x3 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 + 1 (x, y)

–2 y = (–2)3 + 1 = –7 (–2, –7)

–1 y = (–1)3 + 1 = 0 (–1, 0)

0 y = 03 + 1 = 1 (0, 1)

1 y = 13 + 1 = 2 (1, 2)

2 y = 23 + 1 = 9 (2, 9)

78. y = –3x3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –3x3 (x, y)

–2 y = –3(–2)3 = 24 (–2, 24)

–1 y = –3(–1)3 = 3 (–1, 3)

0 y = –3(0)3 = 0 (0, 0)

1 y = –3(1)3 = –3 (1, –3)

2 y = –3(2)3 = –24 (2, –24)

79. y = x3 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 – 4 (x, y)

–2 y = (–2)3 – 4 = –12 (–2, –12)

–1 y = (–1)3 – 4 = –5 (–1, –5)

0 y = 03 – 4 = –4 (0, –4)

1 y = 13 – 4 = –3 (1, –3)

2 y = 23 – 4 = 4 (2, 4)

80. y = 2x + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x + 2 (x, y)

–2 y = 2–2

+ 2 = 2.25 (–2, 2.25)

–1 y = 2–1

+ 2 = 2.5 (–1, 2.5)

0 y = 20+ 2 = 3 (0, 3)

1 y = 21 + 2 = 4 (1, 4)

2 y = 22 + 2 = 6 (2, 6)

81. y = 3x

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x (x, y)

–2 y = 3

–2 =

(–2, )

–1 y = 3

–1 =

(–1, )

0 y = 30 = 1 (0, 1)

1 y = 31 = 3 (1, 3)

2 y = 32 = 9 (2, 9)

82. y = 2x – 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x – 1 (x, y)

–2 y = 2–2

– 1 = –0.75 (–2, –0.75)

–1 y = 2–1

– 1 = –0.5 (–1, –0.5)

0 y = 20 – 1 = 0 (0, 0)

1 y = 21 – 1 = 1 (1, 1)

2 y = 22 – 1 = 3 (2, 3)

83. LIFE SCIENCE Starting from a single bacterium in a dish, the number of bacteria after t cycles of reproduction is

2t. A bacterium reproduces every 30 minutes. If there are 1000 bacteria in a dish now, how many will there be in 1

hour?

SOLUTION:  

To find the number of bacteria will be in the dish in 1 hour, replace t with 2 in the expression 2t because there are 2

thirty minute cycles in 2 hour. Then, multiply the result by 1000 because there are 1000 bacteria in the dish now.

So, there will be 4000 bacteria in the dish in 1 hour.

eSolutions Manual - Powered by Cognero Page 12

Study Guide and Review

Determine whether each statement is true or false . If false , replace the underlined word or number to make a true statement.

1. The exponent of a number raised to the first power can be omitted.

SOLUTION:  An exponent tells how many times a number is used as a factor. So, the exponent of a number raised to the first power can be omitted. The statement is true.

2. A number is in scientific notation when it does not contain exponents.

SOLUTION:  A number that is expressed as a product of a factor and a power of 10 is written in scientific notation. So, the statement is false. A number is in standard form when it does not contain exponents.

3. In 57, the number 7 is the base.

SOLUTION:  

The number that is multiplied is called the base. So, the statement is false. In 57, the number 7 is the exponent.

4. The number 49 is an example of a(n) prime number.

SOLUTION:  A prime number is a whole number that has exactly two unique factors, 1 and itself. So, the statement is false. The number 49 is an example of a composite number.

5. The equation y = 5x + 2 is an example of a(n) exponential function.

SOLUTION:  

An exponential function is a function that can be described by an equation of the form y = ax + c, where a ≠ 0 and 

a ≠ 1. So, the statement is true.

6. The graph of a(n) cubic function is called a parabola.

SOLUTION:  The statement is false. The graph of a quadratic function is called a parabola.

7. To multiply powers with the same base, add the exponents.

SOLUTION:  The statement is true.

8. A(n) nonlinear function has a constant rate of change.

SOLUTION:  Nonlinear functions do not have constant rates of change. So, the statement is false. A linear function has a constant rate of change.

9. To simplify (n6)5, the first step is to add 6 and 5.

SOLUTION:  

To find the power of a power, multiply exponents. So, the statement is false. To simplify (n6)5, the first step is to

multiply 6 and 5.

10. The graph of a(n) quadratic function is symmetric.

SOLUTION:  The graph of a quadratic function is a parabola, which is symmetric. So, the statement is true.

Write each expression using exponents.11. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

12. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

13. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

14. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

15. 35

SOLUTION:  

16. 2 • 43

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

17. x2 – 6

SOLUTION:  

18. w3 + y2

SOLUTION:  

19. 2(y + z3)

SOLUTION:  

20. w4x

2yz

SOLUTION:  

21. TEETH Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

Write the prime factorization of each number. Use exponents for repeated factors.22. 34

SOLUTION:  34 = 2 • 17

23. 40

SOLUTION:  

24. 63

SOLUTION:  

25. 225

SOLUTION:  

Factor each monomial.26. 18x

SOLUTION:  18x = 2 • 3 • 3 • x

27. 10r2

SOLUTION:  

28. 32pq

SOLUTION:  32pq = 2 • 2 • 2 • 2 • 2 • p • q

29. –25ab2

SOLUTION:  

30. PHOTOGRAPHS Jacy has 24 photographs to put in a rectangular arrangement. In how many different numbers of rows and columns can she display them if each row has the same number of photographs? Name each arrangement.

SOLUTION:  List the different numbers of rows and columns by listing the factors of 24. So, Jacy could form rectangles with the following number of rows and columns: 1 • 24, 24 • 1, 2 • 12, 12 • 2, 3 • 8, 8 • 3, 4 • 6, 6 • 4. There are 8 different arrangements.

Find each product or quotient. Express using exponents.

31. 35 • 3

2

SOLUTION:  

32. (–7) • (–7)4

SOLUTION:  

33. m3 • m6

SOLUTION:  

34. x8 • x

SOLUTION:  

35. (2h7)(6h)

SOLUTION:  

36. (5a3)(–6a

4)

SOLUTION:  

37. 

SOLUTION:  

38. 

SOLUTION:  

39. PLANETS Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how

many times farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by thedistance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Write each expression using a positive exponent.

40. 9–4

SOLUTION:  

9–4

=

41. (–10)–2

SOLUTION:  

(–10)–2

=

42. m–5

SOLUTION:  

m–5 =

Write each fraction as an expression using a negative exponent other than –1.

43. 

SOLUTION:  

= 6–3

44. 

SOLUTION:  

or  or 

45. 

SOLUTION:  

46. MEASUREMENT If 1 millimeter is equal to 10–3

meter and 1 nanometer is equal to 10–9

meter, how many nanometers are in 1 millimeter? Write using a positive exponent.

SOLUTION:  To find the number of nanometers in 1 millimeter, divide the number of millimeters in a meter by the number of nanometers in a meter.

So, there are 106 nanometers in 1 millimeter.

Express each number in standard form.

47. 5.82 × 103

SOLUTION:  

48. 9.0 × 10–2

SOLUTION:  

49. 3.4 × 10–4

SOLUTION:  

50. 1.705 × 105

SOLUTION:  

Express each number in scientific notation.51. 379

SOLUTION:  

52. 26,880

SOLUTION:  

53. 0.0014

SOLUTION:  

54. 0.000561

SOLUTION:  

55. SPACE The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Simplify.

56. (26)3

SOLUTION:  

57. (r2)8

SOLUTION:  

58. (3x7)2

SOLUTION:  

59. (–2n4)6

SOLUTION:  

60. (4a9b)

4

SOLUTION:  

61. (5w5x

8)3

SOLUTION:  

62. GEOMETRY Find the area of the square shown below.

SOLUTION:  

Determine whether each graph, equation, or table represents a linear or nonlinear function. Explain.

63. 

SOLUTION:  The graph is a curve, not a straight line. So, it represents a nonlinear function.

64. 

SOLUTION:  The graph is a line. So, it represents a linear function.

65. y = x

SOLUTION:  

The equation y = x represents a linear function, because it is written in the form y = mx + b.

66. y =  + 1

SOLUTION:  

The equation y =  + 1 represents a nonlinear function, because it cannot be written in the form y = mx + b.

67. 

SOLUTION:  As x increases by 1, y decreases by 2. So, this is a linear function.

68. 

SOLUTION:  As x increases by 1, y increases by 10. So, this is a linear function.

69. SCHOOLS A school district’s spending on students over the last five years is represented by the equation y =

325x2 + 0.2x + 1427. Is this equation linear? Explain.

SOLUTION:  

The equation y = 325x2 + 0.2x + 1427 represents a nonlinear function, because it cannot be written in the form y =

mx + b.

Graph each function.

70. y = 3x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x2 (x, y)

–2 y = 3(–2)2 = 12 (–2, 12)

–1 y = 3(–1)2 = 3 (–1, 3)

0 y = 3(0)2 = 0 (0, 0)

1 y = 3(1)2 = 3 (1, 3)

2 y = 3(2)2 = 12 (2, 12)

71. y = –2x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –2x2 (x, y)

–2 y = –2(–2)2 = –8 (–2, –8)

–1 y = –2(–1)2 = –2 (–1, –2)

0 y = –2(0)2 = 0 (0, 0)

1 y = –2(1)2 = –2 (1, –2)

2 y = –2(2)2 = –8 (2, –8)

72. y = x2 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x2 – 4 (x, y)

–2 y = (–2)2 – 4 = 0 (–2, 0)

–1 y = (–1)2 – 4 = –3 (–1, –3)

0 y = 02 – 4 = –4 (0, –4)

1 y = 12 – 4 = –3 (1, –3)

2 y = 22 – 4 = 0 (2, 0)

73. y = –x2 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –x2 + 1 (x, y)

–2 y = –(–2)2 + 1 = –3 (–2, –3)

–1 y = –(–1)2 + 1 = 0 (–1, 0)

0 y = –(0)2 + 1 = 1 (0, 1)

1 y = –(1)2 + 1 = 0 (1, 0)

2 y = –(2)2 + 1 = –3 (2, –3)

74. y = 2x2 + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x2 + 2 (x, y)

–2 y = 2(–2)2 + 2 = 10 (–2, 10)

–1 y = 2(–1)2 + 2 = 4 (–1, 4)

0 y = 2(0)2 + 2 = 2 (0, 2)

1 y = 2(1)2 + 2 = 4 (1, 4)

2 y = 2(2)2 + 2 = 10 (2, 10)

75. y = x2 – 3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x

2 – 3

(x, y)

–2 y = (–2)

2 – 3 = –1

(–2, –1)

–1 y = (–1)

2 – 3 = –2.5

(–1, –2.5)

0 y = (0)

2 – 3 = –3

(0, –3)

1 y = (1)

2 – 3 = –2.5

(1, –2.5)

2 y = (2)

2 – 3 = –1

(2, –1)

76. GEOMETRY The volume of a cylinder with a height of 8 inches can be found using the equation V = 8(3.14)r2

where r is the radius of the cylinder. Graph the equation.

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

r V = 8(3.14)r2 (r, V)

0 V = 8(3.14)(02) = 0 (0, 0)

1 V = 8(3.14)(12) = 25.12 (1, 25.12)

2 V = 8(3.14)(22) = 100.48 (2, 100.48)

3 V = 8(3.14)(32) = 226.08 (3, 226.08)

4 V = 8(3.14)(42) = 401.92 (4, 401.92)

Graph each function.

77. y = x3 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 + 1 (x, y)

–2 y = (–2)3 + 1 = –7 (–2, –7)

–1 y = (–1)3 + 1 = 0 (–1, 0)

0 y = 03 + 1 = 1 (0, 1)

1 y = 13 + 1 = 2 (1, 2)

2 y = 23 + 1 = 9 (2, 9)

78. y = –3x3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –3x3 (x, y)

–2 y = –3(–2)3 = 24 (–2, 24)

–1 y = –3(–1)3 = 3 (–1, 3)

0 y = –3(0)3 = 0 (0, 0)

1 y = –3(1)3 = –3 (1, –3)

2 y = –3(2)3 = –24 (2, –24)

79. y = x3 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 – 4 (x, y)

–2 y = (–2)3 – 4 = –12 (–2, –12)

–1 y = (–1)3 – 4 = –5 (–1, –5)

0 y = 03 – 4 = –4 (0, –4)

1 y = 13 – 4 = –3 (1, –3)

2 y = 23 – 4 = 4 (2, 4)

80. y = 2x + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x + 2 (x, y)

–2 y = 2–2

+ 2 = 2.25 (–2, 2.25)

–1 y = 2–1

+ 2 = 2.5 (–1, 2.5)

0 y = 20+ 2 = 3 (0, 3)

1 y = 21 + 2 = 4 (1, 4)

2 y = 22 + 2 = 6 (2, 6)

81. y = 3x

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x (x, y)

–2 y = 3

–2 =

(–2, )

–1 y = 3

–1 =

(–1, )

0 y = 30 = 1 (0, 1)

1 y = 31 = 3 (1, 3)

2 y = 32 = 9 (2, 9)

82. y = 2x – 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x – 1 (x, y)

–2 y = 2–2

– 1 = –0.75 (–2, –0.75)

–1 y = 2–1

– 1 = –0.5 (–1, –0.5)

0 y = 20 – 1 = 0 (0, 0)

1 y = 21 – 1 = 1 (1, 1)

2 y = 22 – 1 = 3 (2, 3)

83. LIFE SCIENCE Starting from a single bacterium in a dish, the number of bacteria after t cycles of reproduction is

2t. A bacterium reproduces every 30 minutes. If there are 1000 bacteria in a dish now, how many will there be in 1

hour?

SOLUTION:  

To find the number of bacteria will be in the dish in 1 hour, replace t with 2 in the expression 2t because there are 2

thirty minute cycles in 2 hour. Then, multiply the result by 1000 because there are 1000 bacteria in the dish now.

So, there will be 4000 bacteria in the dish in 1 hour.

eSolutions Manual - Powered by Cognero Page 13

Study Guide and Review

Determine whether each statement is true or false . If false , replace the underlined word or number to make a true statement.

1. The exponent of a number raised to the first power can be omitted.

SOLUTION:  An exponent tells how many times a number is used as a factor. So, the exponent of a number raised to the first power can be omitted. The statement is true.

2. A number is in scientific notation when it does not contain exponents.

SOLUTION:  A number that is expressed as a product of a factor and a power of 10 is written in scientific notation. So, the statement is false. A number is in standard form when it does not contain exponents.

3. In 57, the number 7 is the base.

SOLUTION:  

The number that is multiplied is called the base. So, the statement is false. In 57, the number 7 is the exponent.

4. The number 49 is an example of a(n) prime number.

SOLUTION:  A prime number is a whole number that has exactly two unique factors, 1 and itself. So, the statement is false. The number 49 is an example of a composite number.

5. The equation y = 5x + 2 is an example of a(n) exponential function.

SOLUTION:  

An exponential function is a function that can be described by an equation of the form y = ax + c, where a ≠ 0 and 

a ≠ 1. So, the statement is true.

6. The graph of a(n) cubic function is called a parabola.

SOLUTION:  The statement is false. The graph of a quadratic function is called a parabola.

7. To multiply powers with the same base, add the exponents.

SOLUTION:  The statement is true.

8. A(n) nonlinear function has a constant rate of change.

SOLUTION:  Nonlinear functions do not have constant rates of change. So, the statement is false. A linear function has a constant rate of change.

9. To simplify (n6)5, the first step is to add 6 and 5.

SOLUTION:  

To find the power of a power, multiply exponents. So, the statement is false. To simplify (n6)5, the first step is to

multiply 6 and 5.

10. The graph of a(n) quadratic function is symmetric.

SOLUTION:  The graph of a quadratic function is a parabola, which is symmetric. So, the statement is true.

Write each expression using exponents.11. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

12. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

13. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

14. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

15. 35

SOLUTION:  

16. 2 • 43

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

17. x2 – 6

SOLUTION:  

18. w3 + y2

SOLUTION:  

19. 2(y + z3)

SOLUTION:  

20. w4x

2yz

SOLUTION:  

21. TEETH Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

Write the prime factorization of each number. Use exponents for repeated factors.22. 34

SOLUTION:  34 = 2 • 17

23. 40

SOLUTION:  

24. 63

SOLUTION:  

25. 225

SOLUTION:  

Factor each monomial.26. 18x

SOLUTION:  18x = 2 • 3 • 3 • x

27. 10r2

SOLUTION:  

28. 32pq

SOLUTION:  32pq = 2 • 2 • 2 • 2 • 2 • p • q

29. –25ab2

SOLUTION:  

30. PHOTOGRAPHS Jacy has 24 photographs to put in a rectangular arrangement. In how many different numbers of rows and columns can she display them if each row has the same number of photographs? Name each arrangement.

SOLUTION:  List the different numbers of rows and columns by listing the factors of 24. So, Jacy could form rectangles with the following number of rows and columns: 1 • 24, 24 • 1, 2 • 12, 12 • 2, 3 • 8, 8 • 3, 4 • 6, 6 • 4. There are 8 different arrangements.

Find each product or quotient. Express using exponents.

31. 35 • 3

2

SOLUTION:  

32. (–7) • (–7)4

SOLUTION:  

33. m3 • m6

SOLUTION:  

34. x8 • x

SOLUTION:  

35. (2h7)(6h)

SOLUTION:  

36. (5a3)(–6a

4)

SOLUTION:  

37. 

SOLUTION:  

38. 

SOLUTION:  

39. PLANETS Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how

many times farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by thedistance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Write each expression using a positive exponent.

40. 9–4

SOLUTION:  

9–4

=

41. (–10)–2

SOLUTION:  

(–10)–2

=

42. m–5

SOLUTION:  

m–5 =

Write each fraction as an expression using a negative exponent other than –1.

43. 

SOLUTION:  

= 6–3

44. 

SOLUTION:  

or  or 

45. 

SOLUTION:  

46. MEASUREMENT If 1 millimeter is equal to 10–3

meter and 1 nanometer is equal to 10–9

meter, how many nanometers are in 1 millimeter? Write using a positive exponent.

SOLUTION:  To find the number of nanometers in 1 millimeter, divide the number of millimeters in a meter by the number of nanometers in a meter.

So, there are 106 nanometers in 1 millimeter.

Express each number in standard form.

47. 5.82 × 103

SOLUTION:  

48. 9.0 × 10–2

SOLUTION:  

49. 3.4 × 10–4

SOLUTION:  

50. 1.705 × 105

SOLUTION:  

Express each number in scientific notation.51. 379

SOLUTION:  

52. 26,880

SOLUTION:  

53. 0.0014

SOLUTION:  

54. 0.000561

SOLUTION:  

55. SPACE The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Simplify.

56. (26)3

SOLUTION:  

57. (r2)8

SOLUTION:  

58. (3x7)2

SOLUTION:  

59. (–2n4)6

SOLUTION:  

60. (4a9b)

4

SOLUTION:  

61. (5w5x

8)3

SOLUTION:  

62. GEOMETRY Find the area of the square shown below.

SOLUTION:  

Determine whether each graph, equation, or table represents a linear or nonlinear function. Explain.

63. 

SOLUTION:  The graph is a curve, not a straight line. So, it represents a nonlinear function.

64. 

SOLUTION:  The graph is a line. So, it represents a linear function.

65. y = x

SOLUTION:  

The equation y = x represents a linear function, because it is written in the form y = mx + b.

66. y =  + 1

SOLUTION:  

The equation y =  + 1 represents a nonlinear function, because it cannot be written in the form y = mx + b.

67. 

SOLUTION:  As x increases by 1, y decreases by 2. So, this is a linear function.

68. 

SOLUTION:  As x increases by 1, y increases by 10. So, this is a linear function.

69. SCHOOLS A school district’s spending on students over the last five years is represented by the equation y =

325x2 + 0.2x + 1427. Is this equation linear? Explain.

SOLUTION:  

The equation y = 325x2 + 0.2x + 1427 represents a nonlinear function, because it cannot be written in the form y =

mx + b.

Graph each function.

70. y = 3x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x2 (x, y)

–2 y = 3(–2)2 = 12 (–2, 12)

–1 y = 3(–1)2 = 3 (–1, 3)

0 y = 3(0)2 = 0 (0, 0)

1 y = 3(1)2 = 3 (1, 3)

2 y = 3(2)2 = 12 (2, 12)

71. y = –2x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –2x2 (x, y)

–2 y = –2(–2)2 = –8 (–2, –8)

–1 y = –2(–1)2 = –2 (–1, –2)

0 y = –2(0)2 = 0 (0, 0)

1 y = –2(1)2 = –2 (1, –2)

2 y = –2(2)2 = –8 (2, –8)

72. y = x2 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x2 – 4 (x, y)

–2 y = (–2)2 – 4 = 0 (–2, 0)

–1 y = (–1)2 – 4 = –3 (–1, –3)

0 y = 02 – 4 = –4 (0, –4)

1 y = 12 – 4 = –3 (1, –3)

2 y = 22 – 4 = 0 (2, 0)

73. y = –x2 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –x2 + 1 (x, y)

–2 y = –(–2)2 + 1 = –3 (–2, –3)

–1 y = –(–1)2 + 1 = 0 (–1, 0)

0 y = –(0)2 + 1 = 1 (0, 1)

1 y = –(1)2 + 1 = 0 (1, 0)

2 y = –(2)2 + 1 = –3 (2, –3)

74. y = 2x2 + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x2 + 2 (x, y)

–2 y = 2(–2)2 + 2 = 10 (–2, 10)

–1 y = 2(–1)2 + 2 = 4 (–1, 4)

0 y = 2(0)2 + 2 = 2 (0, 2)

1 y = 2(1)2 + 2 = 4 (1, 4)

2 y = 2(2)2 + 2 = 10 (2, 10)

75. y = x2 – 3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x

2 – 3

(x, y)

–2 y = (–2)

2 – 3 = –1

(–2, –1)

–1 y = (–1)

2 – 3 = –2.5

(–1, –2.5)

0 y = (0)

2 – 3 = –3

(0, –3)

1 y = (1)

2 – 3 = –2.5

(1, –2.5)

2 y = (2)

2 – 3 = –1

(2, –1)

76. GEOMETRY The volume of a cylinder with a height of 8 inches can be found using the equation V = 8(3.14)r2

where r is the radius of the cylinder. Graph the equation.

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

r V = 8(3.14)r2 (r, V)

0 V = 8(3.14)(02) = 0 (0, 0)

1 V = 8(3.14)(12) = 25.12 (1, 25.12)

2 V = 8(3.14)(22) = 100.48 (2, 100.48)

3 V = 8(3.14)(32) = 226.08 (3, 226.08)

4 V = 8(3.14)(42) = 401.92 (4, 401.92)

Graph each function.

77. y = x3 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 + 1 (x, y)

–2 y = (–2)3 + 1 = –7 (–2, –7)

–1 y = (–1)3 + 1 = 0 (–1, 0)

0 y = 03 + 1 = 1 (0, 1)

1 y = 13 + 1 = 2 (1, 2)

2 y = 23 + 1 = 9 (2, 9)

78. y = –3x3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –3x3 (x, y)

–2 y = –3(–2)3 = 24 (–2, 24)

–1 y = –3(–1)3 = 3 (–1, 3)

0 y = –3(0)3 = 0 (0, 0)

1 y = –3(1)3 = –3 (1, –3)

2 y = –3(2)3 = –24 (2, –24)

79. y = x3 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 – 4 (x, y)

–2 y = (–2)3 – 4 = –12 (–2, –12)

–1 y = (–1)3 – 4 = –5 (–1, –5)

0 y = 03 – 4 = –4 (0, –4)

1 y = 13 – 4 = –3 (1, –3)

2 y = 23 – 4 = 4 (2, 4)

80. y = 2x + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x + 2 (x, y)

–2 y = 2–2

+ 2 = 2.25 (–2, 2.25)

–1 y = 2–1

+ 2 = 2.5 (–1, 2.5)

0 y = 20+ 2 = 3 (0, 3)

1 y = 21 + 2 = 4 (1, 4)

2 y = 22 + 2 = 6 (2, 6)

81. y = 3x

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x (x, y)

–2 y = 3

–2 =

(–2, )

–1 y = 3

–1 =

(–1, )

0 y = 30 = 1 (0, 1)

1 y = 31 = 3 (1, 3)

2 y = 32 = 9 (2, 9)

82. y = 2x – 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x – 1 (x, y)

–2 y = 2–2

– 1 = –0.75 (–2, –0.75)

–1 y = 2–1

– 1 = –0.5 (–1, –0.5)

0 y = 20 – 1 = 0 (0, 0)

1 y = 21 – 1 = 1 (1, 1)

2 y = 22 – 1 = 3 (2, 3)

83. LIFE SCIENCE Starting from a single bacterium in a dish, the number of bacteria after t cycles of reproduction is

2t. A bacterium reproduces every 30 minutes. If there are 1000 bacteria in a dish now, how many will there be in 1

hour?

SOLUTION:  

To find the number of bacteria will be in the dish in 1 hour, replace t with 2 in the expression 2t because there are 2

thirty minute cycles in 2 hour. Then, multiply the result by 1000 because there are 1000 bacteria in the dish now.

So, there will be 4000 bacteria in the dish in 1 hour.

eSolutions Manual - Powered by Cognero Page 14

Study Guide and Review

Determine whether each statement is true or false . If false , replace the underlined word or number to make a true statement.

1. The exponent of a number raised to the first power can be omitted.

SOLUTION:  An exponent tells how many times a number is used as a factor. So, the exponent of a number raised to the first power can be omitted. The statement is true.

2. A number is in scientific notation when it does not contain exponents.

SOLUTION:  A number that is expressed as a product of a factor and a power of 10 is written in scientific notation. So, the statement is false. A number is in standard form when it does not contain exponents.

3. In 57, the number 7 is the base.

SOLUTION:  

The number that is multiplied is called the base. So, the statement is false. In 57, the number 7 is the exponent.

4. The number 49 is an example of a(n) prime number.

SOLUTION:  A prime number is a whole number that has exactly two unique factors, 1 and itself. So, the statement is false. The number 49 is an example of a composite number.

5. The equation y = 5x + 2 is an example of a(n) exponential function.

SOLUTION:  

An exponential function is a function that can be described by an equation of the form y = ax + c, where a ≠ 0 and 

a ≠ 1. So, the statement is true.

6. The graph of a(n) cubic function is called a parabola.

SOLUTION:  The statement is false. The graph of a quadratic function is called a parabola.

7. To multiply powers with the same base, add the exponents.

SOLUTION:  The statement is true.

8. A(n) nonlinear function has a constant rate of change.

SOLUTION:  Nonlinear functions do not have constant rates of change. So, the statement is false. A linear function has a constant rate of change.

9. To simplify (n6)5, the first step is to add 6 and 5.

SOLUTION:  

To find the power of a power, multiply exponents. So, the statement is false. To simplify (n6)5, the first step is to

multiply 6 and 5.

10. The graph of a(n) quadratic function is symmetric.

SOLUTION:  The graph of a quadratic function is a parabola, which is symmetric. So, the statement is true.

Write each expression using exponents.11. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

12. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

13. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

14. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

15. 35

SOLUTION:  

16. 2 • 43

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

17. x2 – 6

SOLUTION:  

18. w3 + y2

SOLUTION:  

19. 2(y + z3)

SOLUTION:  

20. w4x

2yz

SOLUTION:  

21. TEETH Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

Write the prime factorization of each number. Use exponents for repeated factors.22. 34

SOLUTION:  34 = 2 • 17

23. 40

SOLUTION:  

24. 63

SOLUTION:  

25. 225

SOLUTION:  

Factor each monomial.26. 18x

SOLUTION:  18x = 2 • 3 • 3 • x

27. 10r2

SOLUTION:  

28. 32pq

SOLUTION:  32pq = 2 • 2 • 2 • 2 • 2 • p • q

29. –25ab2

SOLUTION:  

30. PHOTOGRAPHS Jacy has 24 photographs to put in a rectangular arrangement. In how many different numbers of rows and columns can she display them if each row has the same number of photographs? Name each arrangement.

SOLUTION:  List the different numbers of rows and columns by listing the factors of 24. So, Jacy could form rectangles with the following number of rows and columns: 1 • 24, 24 • 1, 2 • 12, 12 • 2, 3 • 8, 8 • 3, 4 • 6, 6 • 4. There are 8 different arrangements.

Find each product or quotient. Express using exponents.

31. 35 • 3

2

SOLUTION:  

32. (–7) • (–7)4

SOLUTION:  

33. m3 • m6

SOLUTION:  

34. x8 • x

SOLUTION:  

35. (2h7)(6h)

SOLUTION:  

36. (5a3)(–6a

4)

SOLUTION:  

37. 

SOLUTION:  

38. 

SOLUTION:  

39. PLANETS Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how

many times farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by thedistance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Write each expression using a positive exponent.

40. 9–4

SOLUTION:  

9–4

=

41. (–10)–2

SOLUTION:  

(–10)–2

=

42. m–5

SOLUTION:  

m–5 =

Write each fraction as an expression using a negative exponent other than –1.

43. 

SOLUTION:  

= 6–3

44. 

SOLUTION:  

or  or 

45. 

SOLUTION:  

46. MEASUREMENT If 1 millimeter is equal to 10–3

meter and 1 nanometer is equal to 10–9

meter, how many nanometers are in 1 millimeter? Write using a positive exponent.

SOLUTION:  To find the number of nanometers in 1 millimeter, divide the number of millimeters in a meter by the number of nanometers in a meter.

So, there are 106 nanometers in 1 millimeter.

Express each number in standard form.

47. 5.82 × 103

SOLUTION:  

48. 9.0 × 10–2

SOLUTION:  

49. 3.4 × 10–4

SOLUTION:  

50. 1.705 × 105

SOLUTION:  

Express each number in scientific notation.51. 379

SOLUTION:  

52. 26,880

SOLUTION:  

53. 0.0014

SOLUTION:  

54. 0.000561

SOLUTION:  

55. SPACE The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Simplify.

56. (26)3

SOLUTION:  

57. (r2)8

SOLUTION:  

58. (3x7)2

SOLUTION:  

59. (–2n4)6

SOLUTION:  

60. (4a9b)

4

SOLUTION:  

61. (5w5x

8)3

SOLUTION:  

62. GEOMETRY Find the area of the square shown below.

SOLUTION:  

Determine whether each graph, equation, or table represents a linear or nonlinear function. Explain.

63. 

SOLUTION:  The graph is a curve, not a straight line. So, it represents a nonlinear function.

64. 

SOLUTION:  The graph is a line. So, it represents a linear function.

65. y = x

SOLUTION:  

The equation y = x represents a linear function, because it is written in the form y = mx + b.

66. y =  + 1

SOLUTION:  

The equation y =  + 1 represents a nonlinear function, because it cannot be written in the form y = mx + b.

67. 

SOLUTION:  As x increases by 1, y decreases by 2. So, this is a linear function.

68. 

SOLUTION:  As x increases by 1, y increases by 10. So, this is a linear function.

69. SCHOOLS A school district’s spending on students over the last five years is represented by the equation y =

325x2 + 0.2x + 1427. Is this equation linear? Explain.

SOLUTION:  

The equation y = 325x2 + 0.2x + 1427 represents a nonlinear function, because it cannot be written in the form y =

mx + b.

Graph each function.

70. y = 3x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x2 (x, y)

–2 y = 3(–2)2 = 12 (–2, 12)

–1 y = 3(–1)2 = 3 (–1, 3)

0 y = 3(0)2 = 0 (0, 0)

1 y = 3(1)2 = 3 (1, 3)

2 y = 3(2)2 = 12 (2, 12)

71. y = –2x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –2x2 (x, y)

–2 y = –2(–2)2 = –8 (–2, –8)

–1 y = –2(–1)2 = –2 (–1, –2)

0 y = –2(0)2 = 0 (0, 0)

1 y = –2(1)2 = –2 (1, –2)

2 y = –2(2)2 = –8 (2, –8)

72. y = x2 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x2 – 4 (x, y)

–2 y = (–2)2 – 4 = 0 (–2, 0)

–1 y = (–1)2 – 4 = –3 (–1, –3)

0 y = 02 – 4 = –4 (0, –4)

1 y = 12 – 4 = –3 (1, –3)

2 y = 22 – 4 = 0 (2, 0)

73. y = –x2 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –x2 + 1 (x, y)

–2 y = –(–2)2 + 1 = –3 (–2, –3)

–1 y = –(–1)2 + 1 = 0 (–1, 0)

0 y = –(0)2 + 1 = 1 (0, 1)

1 y = –(1)2 + 1 = 0 (1, 0)

2 y = –(2)2 + 1 = –3 (2, –3)

74. y = 2x2 + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x2 + 2 (x, y)

–2 y = 2(–2)2 + 2 = 10 (–2, 10)

–1 y = 2(–1)2 + 2 = 4 (–1, 4)

0 y = 2(0)2 + 2 = 2 (0, 2)

1 y = 2(1)2 + 2 = 4 (1, 4)

2 y = 2(2)2 + 2 = 10 (2, 10)

75. y = x2 – 3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x

2 – 3

(x, y)

–2 y = (–2)

2 – 3 = –1

(–2, –1)

–1 y = (–1)

2 – 3 = –2.5

(–1, –2.5)

0 y = (0)

2 – 3 = –3

(0, –3)

1 y = (1)

2 – 3 = –2.5

(1, –2.5)

2 y = (2)

2 – 3 = –1

(2, –1)

76. GEOMETRY The volume of a cylinder with a height of 8 inches can be found using the equation V = 8(3.14)r2

where r is the radius of the cylinder. Graph the equation.

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

r V = 8(3.14)r2 (r, V)

0 V = 8(3.14)(02) = 0 (0, 0)

1 V = 8(3.14)(12) = 25.12 (1, 25.12)

2 V = 8(3.14)(22) = 100.48 (2, 100.48)

3 V = 8(3.14)(32) = 226.08 (3, 226.08)

4 V = 8(3.14)(42) = 401.92 (4, 401.92)

Graph each function.

77. y = x3 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 + 1 (x, y)

–2 y = (–2)3 + 1 = –7 (–2, –7)

–1 y = (–1)3 + 1 = 0 (–1, 0)

0 y = 03 + 1 = 1 (0, 1)

1 y = 13 + 1 = 2 (1, 2)

2 y = 23 + 1 = 9 (2, 9)

78. y = –3x3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –3x3 (x, y)

–2 y = –3(–2)3 = 24 (–2, 24)

–1 y = –3(–1)3 = 3 (–1, 3)

0 y = –3(0)3 = 0 (0, 0)

1 y = –3(1)3 = –3 (1, –3)

2 y = –3(2)3 = –24 (2, –24)

79. y = x3 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 – 4 (x, y)

–2 y = (–2)3 – 4 = –12 (–2, –12)

–1 y = (–1)3 – 4 = –5 (–1, –5)

0 y = 03 – 4 = –4 (0, –4)

1 y = 13 – 4 = –3 (1, –3)

2 y = 23 – 4 = 4 (2, 4)

80. y = 2x + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x + 2 (x, y)

–2 y = 2–2

+ 2 = 2.25 (–2, 2.25)

–1 y = 2–1

+ 2 = 2.5 (–1, 2.5)

0 y = 20+ 2 = 3 (0, 3)

1 y = 21 + 2 = 4 (1, 4)

2 y = 22 + 2 = 6 (2, 6)

81. y = 3x

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x (x, y)

–2 y = 3

–2 =

(–2, )

–1 y = 3

–1 =

(–1, )

0 y = 30 = 1 (0, 1)

1 y = 31 = 3 (1, 3)

2 y = 32 = 9 (2, 9)

82. y = 2x – 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x – 1 (x, y)

–2 y = 2–2

– 1 = –0.75 (–2, –0.75)

–1 y = 2–1

– 1 = –0.5 (–1, –0.5)

0 y = 20 – 1 = 0 (0, 0)

1 y = 21 – 1 = 1 (1, 1)

2 y = 22 – 1 = 3 (2, 3)

83. LIFE SCIENCE Starting from a single bacterium in a dish, the number of bacteria after t cycles of reproduction is

2t. A bacterium reproduces every 30 minutes. If there are 1000 bacteria in a dish now, how many will there be in 1

hour?

SOLUTION:  

To find the number of bacteria will be in the dish in 1 hour, replace t with 2 in the expression 2t because there are 2

thirty minute cycles in 2 hour. Then, multiply the result by 1000 because there are 1000 bacteria in the dish now.

So, there will be 4000 bacteria in the dish in 1 hour.

eSolutions Manual - Powered by Cognero Page 15

Study Guide and Review

Determine whether each statement is true or false . If false , replace the underlined word or number to make a true statement.

1. The exponent of a number raised to the first power can be omitted.

SOLUTION:  An exponent tells how many times a number is used as a factor. So, the exponent of a number raised to the first power can be omitted. The statement is true.

2. A number is in scientific notation when it does not contain exponents.

SOLUTION:  A number that is expressed as a product of a factor and a power of 10 is written in scientific notation. So, the statement is false. A number is in standard form when it does not contain exponents.

3. In 57, the number 7 is the base.

SOLUTION:  

The number that is multiplied is called the base. So, the statement is false. In 57, the number 7 is the exponent.

4. The number 49 is an example of a(n) prime number.

SOLUTION:  A prime number is a whole number that has exactly two unique factors, 1 and itself. So, the statement is false. The number 49 is an example of a composite number.

5. The equation y = 5x + 2 is an example of a(n) exponential function.

SOLUTION:  

An exponential function is a function that can be described by an equation of the form y = ax + c, where a ≠ 0 and 

a ≠ 1. So, the statement is true.

6. The graph of a(n) cubic function is called a parabola.

SOLUTION:  The statement is false. The graph of a quadratic function is called a parabola.

7. To multiply powers with the same base, add the exponents.

SOLUTION:  The statement is true.

8. A(n) nonlinear function has a constant rate of change.

SOLUTION:  Nonlinear functions do not have constant rates of change. So, the statement is false. A linear function has a constant rate of change.

9. To simplify (n6)5, the first step is to add 6 and 5.

SOLUTION:  

To find the power of a power, multiply exponents. So, the statement is false. To simplify (n6)5, the first step is to

multiply 6 and 5.

10. The graph of a(n) quadratic function is symmetric.

SOLUTION:  The graph of a quadratic function is a parabola, which is symmetric. So, the statement is true.

Write each expression using exponents.11. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

12. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

13. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

14. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

15. 35

SOLUTION:  

16. 2 • 43

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

17. x2 – 6

SOLUTION:  

18. w3 + y2

SOLUTION:  

19. 2(y + z3)

SOLUTION:  

20. w4x

2yz

SOLUTION:  

21. TEETH Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

Write the prime factorization of each number. Use exponents for repeated factors.22. 34

SOLUTION:  34 = 2 • 17

23. 40

SOLUTION:  

24. 63

SOLUTION:  

25. 225

SOLUTION:  

Factor each monomial.26. 18x

SOLUTION:  18x = 2 • 3 • 3 • x

27. 10r2

SOLUTION:  

28. 32pq

SOLUTION:  32pq = 2 • 2 • 2 • 2 • 2 • p • q

29. –25ab2

SOLUTION:  

30. PHOTOGRAPHS Jacy has 24 photographs to put in a rectangular arrangement. In how many different numbers of rows and columns can she display them if each row has the same number of photographs? Name each arrangement.

SOLUTION:  List the different numbers of rows and columns by listing the factors of 24. So, Jacy could form rectangles with the following number of rows and columns: 1 • 24, 24 • 1, 2 • 12, 12 • 2, 3 • 8, 8 • 3, 4 • 6, 6 • 4. There are 8 different arrangements.

Find each product or quotient. Express using exponents.

31. 35 • 3

2

SOLUTION:  

32. (–7) • (–7)4

SOLUTION:  

33. m3 • m6

SOLUTION:  

34. x8 • x

SOLUTION:  

35. (2h7)(6h)

SOLUTION:  

36. (5a3)(–6a

4)

SOLUTION:  

37. 

SOLUTION:  

38. 

SOLUTION:  

39. PLANETS Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how

many times farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by thedistance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Write each expression using a positive exponent.

40. 9–4

SOLUTION:  

9–4

=

41. (–10)–2

SOLUTION:  

(–10)–2

=

42. m–5

SOLUTION:  

m–5 =

Write each fraction as an expression using a negative exponent other than –1.

43. 

SOLUTION:  

= 6–3

44. 

SOLUTION:  

or  or 

45. 

SOLUTION:  

46. MEASUREMENT If 1 millimeter is equal to 10–3

meter and 1 nanometer is equal to 10–9

meter, how many nanometers are in 1 millimeter? Write using a positive exponent.

SOLUTION:  To find the number of nanometers in 1 millimeter, divide the number of millimeters in a meter by the number of nanometers in a meter.

So, there are 106 nanometers in 1 millimeter.

Express each number in standard form.

47. 5.82 × 103

SOLUTION:  

48. 9.0 × 10–2

SOLUTION:  

49. 3.4 × 10–4

SOLUTION:  

50. 1.705 × 105

SOLUTION:  

Express each number in scientific notation.51. 379

SOLUTION:  

52. 26,880

SOLUTION:  

53. 0.0014

SOLUTION:  

54. 0.000561

SOLUTION:  

55. SPACE The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Simplify.

56. (26)3

SOLUTION:  

57. (r2)8

SOLUTION:  

58. (3x7)2

SOLUTION:  

59. (–2n4)6

SOLUTION:  

60. (4a9b)

4

SOLUTION:  

61. (5w5x

8)3

SOLUTION:  

62. GEOMETRY Find the area of the square shown below.

SOLUTION:  

Determine whether each graph, equation, or table represents a linear or nonlinear function. Explain.

63. 

SOLUTION:  The graph is a curve, not a straight line. So, it represents a nonlinear function.

64. 

SOLUTION:  The graph is a line. So, it represents a linear function.

65. y = x

SOLUTION:  

The equation y = x represents a linear function, because it is written in the form y = mx + b.

66. y =  + 1

SOLUTION:  

The equation y =  + 1 represents a nonlinear function, because it cannot be written in the form y = mx + b.

67. 

SOLUTION:  As x increases by 1, y decreases by 2. So, this is a linear function.

68. 

SOLUTION:  As x increases by 1, y increases by 10. So, this is a linear function.

69. SCHOOLS A school district’s spending on students over the last five years is represented by the equation y =

325x2 + 0.2x + 1427. Is this equation linear? Explain.

SOLUTION:  

The equation y = 325x2 + 0.2x + 1427 represents a nonlinear function, because it cannot be written in the form y =

mx + b.

Graph each function.

70. y = 3x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x2 (x, y)

–2 y = 3(–2)2 = 12 (–2, 12)

–1 y = 3(–1)2 = 3 (–1, 3)

0 y = 3(0)2 = 0 (0, 0)

1 y = 3(1)2 = 3 (1, 3)

2 y = 3(2)2 = 12 (2, 12)

71. y = –2x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –2x2 (x, y)

–2 y = –2(–2)2 = –8 (–2, –8)

–1 y = –2(–1)2 = –2 (–1, –2)

0 y = –2(0)2 = 0 (0, 0)

1 y = –2(1)2 = –2 (1, –2)

2 y = –2(2)2 = –8 (2, –8)

72. y = x2 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x2 – 4 (x, y)

–2 y = (–2)2 – 4 = 0 (–2, 0)

–1 y = (–1)2 – 4 = –3 (–1, –3)

0 y = 02 – 4 = –4 (0, –4)

1 y = 12 – 4 = –3 (1, –3)

2 y = 22 – 4 = 0 (2, 0)

73. y = –x2 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –x2 + 1 (x, y)

–2 y = –(–2)2 + 1 = –3 (–2, –3)

–1 y = –(–1)2 + 1 = 0 (–1, 0)

0 y = –(0)2 + 1 = 1 (0, 1)

1 y = –(1)2 + 1 = 0 (1, 0)

2 y = –(2)2 + 1 = –3 (2, –3)

74. y = 2x2 + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x2 + 2 (x, y)

–2 y = 2(–2)2 + 2 = 10 (–2, 10)

–1 y = 2(–1)2 + 2 = 4 (–1, 4)

0 y = 2(0)2 + 2 = 2 (0, 2)

1 y = 2(1)2 + 2 = 4 (1, 4)

2 y = 2(2)2 + 2 = 10 (2, 10)

75. y = x2 – 3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x

2 – 3

(x, y)

–2 y = (–2)

2 – 3 = –1

(–2, –1)

–1 y = (–1)

2 – 3 = –2.5

(–1, –2.5)

0 y = (0)

2 – 3 = –3

(0, –3)

1 y = (1)

2 – 3 = –2.5

(1, –2.5)

2 y = (2)

2 – 3 = –1

(2, –1)

76. GEOMETRY The volume of a cylinder with a height of 8 inches can be found using the equation V = 8(3.14)r2

where r is the radius of the cylinder. Graph the equation.

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

r V = 8(3.14)r2 (r, V)

0 V = 8(3.14)(02) = 0 (0, 0)

1 V = 8(3.14)(12) = 25.12 (1, 25.12)

2 V = 8(3.14)(22) = 100.48 (2, 100.48)

3 V = 8(3.14)(32) = 226.08 (3, 226.08)

4 V = 8(3.14)(42) = 401.92 (4, 401.92)

Graph each function.

77. y = x3 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 + 1 (x, y)

–2 y = (–2)3 + 1 = –7 (–2, –7)

–1 y = (–1)3 + 1 = 0 (–1, 0)

0 y = 03 + 1 = 1 (0, 1)

1 y = 13 + 1 = 2 (1, 2)

2 y = 23 + 1 = 9 (2, 9)

78. y = –3x3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –3x3 (x, y)

–2 y = –3(–2)3 = 24 (–2, 24)

–1 y = –3(–1)3 = 3 (–1, 3)

0 y = –3(0)3 = 0 (0, 0)

1 y = –3(1)3 = –3 (1, –3)

2 y = –3(2)3 = –24 (2, –24)

79. y = x3 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 – 4 (x, y)

–2 y = (–2)3 – 4 = –12 (–2, –12)

–1 y = (–1)3 – 4 = –5 (–1, –5)

0 y = 03 – 4 = –4 (0, –4)

1 y = 13 – 4 = –3 (1, –3)

2 y = 23 – 4 = 4 (2, 4)

80. y = 2x + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x + 2 (x, y)

–2 y = 2–2

+ 2 = 2.25 (–2, 2.25)

–1 y = 2–1

+ 2 = 2.5 (–1, 2.5)

0 y = 20+ 2 = 3 (0, 3)

1 y = 21 + 2 = 4 (1, 4)

2 y = 22 + 2 = 6 (2, 6)

81. y = 3x

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x (x, y)

–2 y = 3

–2 =

(–2, )

–1 y = 3

–1 =

(–1, )

0 y = 30 = 1 (0, 1)

1 y = 31 = 3 (1, 3)

2 y = 32 = 9 (2, 9)

82. y = 2x – 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x – 1 (x, y)

–2 y = 2–2

– 1 = –0.75 (–2, –0.75)

–1 y = 2–1

– 1 = –0.5 (–1, –0.5)

0 y = 20 – 1 = 0 (0, 0)

1 y = 21 – 1 = 1 (1, 1)

2 y = 22 – 1 = 3 (2, 3)

83. LIFE SCIENCE Starting from a single bacterium in a dish, the number of bacteria after t cycles of reproduction is

2t. A bacterium reproduces every 30 minutes. If there are 1000 bacteria in a dish now, how many will there be in 1

hour?

SOLUTION:  

To find the number of bacteria will be in the dish in 1 hour, replace t with 2 in the expression 2t because there are 2

thirty minute cycles in 2 hour. Then, multiply the result by 1000 because there are 1000 bacteria in the dish now.

So, there will be 4000 bacteria in the dish in 1 hour.

eSolutions Manual - Powered by Cognero Page 16

Study Guide and Review

Determine whether each statement is true or false . If false , replace the underlined word or number to make a true statement.

1. The exponent of a number raised to the first power can be omitted.

SOLUTION:  An exponent tells how many times a number is used as a factor. So, the exponent of a number raised to the first power can be omitted. The statement is true.

2. A number is in scientific notation when it does not contain exponents.

SOLUTION:  A number that is expressed as a product of a factor and a power of 10 is written in scientific notation. So, the statement is false. A number is in standard form when it does not contain exponents.

3. In 57, the number 7 is the base.

SOLUTION:  

The number that is multiplied is called the base. So, the statement is false. In 57, the number 7 is the exponent.

4. The number 49 is an example of a(n) prime number.

SOLUTION:  A prime number is a whole number that has exactly two unique factors, 1 and itself. So, the statement is false. The number 49 is an example of a composite number.

5. The equation y = 5x + 2 is an example of a(n) exponential function.

SOLUTION:  

An exponential function is a function that can be described by an equation of the form y = ax + c, where a ≠ 0 and 

a ≠ 1. So, the statement is true.

6. The graph of a(n) cubic function is called a parabola.

SOLUTION:  The statement is false. The graph of a quadratic function is called a parabola.

7. To multiply powers with the same base, add the exponents.

SOLUTION:  The statement is true.

8. A(n) nonlinear function has a constant rate of change.

SOLUTION:  Nonlinear functions do not have constant rates of change. So, the statement is false. A linear function has a constant rate of change.

9. To simplify (n6)5, the first step is to add 6 and 5.

SOLUTION:  

To find the power of a power, multiply exponents. So, the statement is false. To simplify (n6)5, the first step is to

multiply 6 and 5.

10. The graph of a(n) quadratic function is symmetric.

SOLUTION:  The graph of a quadratic function is a parabola, which is symmetric. So, the statement is true.

Write each expression using exponents.11. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

12. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

13. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

14. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

15. 35

SOLUTION:  

16. 2 • 43

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

17. x2 – 6

SOLUTION:  

18. w3 + y2

SOLUTION:  

19. 2(y + z3)

SOLUTION:  

20. w4x

2yz

SOLUTION:  

21. TEETH Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

Write the prime factorization of each number. Use exponents for repeated factors.22. 34

SOLUTION:  34 = 2 • 17

23. 40

SOLUTION:  

24. 63

SOLUTION:  

25. 225

SOLUTION:  

Factor each monomial.26. 18x

SOLUTION:  18x = 2 • 3 • 3 • x

27. 10r2

SOLUTION:  

28. 32pq

SOLUTION:  32pq = 2 • 2 • 2 • 2 • 2 • p • q

29. –25ab2

SOLUTION:  

30. PHOTOGRAPHS Jacy has 24 photographs to put in a rectangular arrangement. In how many different numbers of rows and columns can she display them if each row has the same number of photographs? Name each arrangement.

SOLUTION:  List the different numbers of rows and columns by listing the factors of 24. So, Jacy could form rectangles with the following number of rows and columns: 1 • 24, 24 • 1, 2 • 12, 12 • 2, 3 • 8, 8 • 3, 4 • 6, 6 • 4. There are 8 different arrangements.

Find each product or quotient. Express using exponents.

31. 35 • 3

2

SOLUTION:  

32. (–7) • (–7)4

SOLUTION:  

33. m3 • m6

SOLUTION:  

34. x8 • x

SOLUTION:  

35. (2h7)(6h)

SOLUTION:  

36. (5a3)(–6a

4)

SOLUTION:  

37. 

SOLUTION:  

38. 

SOLUTION:  

39. PLANETS Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how

many times farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by thedistance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Write each expression using a positive exponent.

40. 9–4

SOLUTION:  

9–4

=

41. (–10)–2

SOLUTION:  

(–10)–2

=

42. m–5

SOLUTION:  

m–5 =

Write each fraction as an expression using a negative exponent other than –1.

43. 

SOLUTION:  

= 6–3

44. 

SOLUTION:  

or  or 

45. 

SOLUTION:  

46. MEASUREMENT If 1 millimeter is equal to 10–3

meter and 1 nanometer is equal to 10–9

meter, how many nanometers are in 1 millimeter? Write using a positive exponent.

SOLUTION:  To find the number of nanometers in 1 millimeter, divide the number of millimeters in a meter by the number of nanometers in a meter.

So, there are 106 nanometers in 1 millimeter.

Express each number in standard form.

47. 5.82 × 103

SOLUTION:  

48. 9.0 × 10–2

SOLUTION:  

49. 3.4 × 10–4

SOLUTION:  

50. 1.705 × 105

SOLUTION:  

Express each number in scientific notation.51. 379

SOLUTION:  

52. 26,880

SOLUTION:  

53. 0.0014

SOLUTION:  

54. 0.000561

SOLUTION:  

55. SPACE The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Simplify.

56. (26)3

SOLUTION:  

57. (r2)8

SOLUTION:  

58. (3x7)2

SOLUTION:  

59. (–2n4)6

SOLUTION:  

60. (4a9b)

4

SOLUTION:  

61. (5w5x

8)3

SOLUTION:  

62. GEOMETRY Find the area of the square shown below.

SOLUTION:  

Determine whether each graph, equation, or table represents a linear or nonlinear function. Explain.

63. 

SOLUTION:  The graph is a curve, not a straight line. So, it represents a nonlinear function.

64. 

SOLUTION:  The graph is a line. So, it represents a linear function.

65. y = x

SOLUTION:  

The equation y = x represents a linear function, because it is written in the form y = mx + b.

66. y =  + 1

SOLUTION:  

The equation y =  + 1 represents a nonlinear function, because it cannot be written in the form y = mx + b.

67. 

SOLUTION:  As x increases by 1, y decreases by 2. So, this is a linear function.

68. 

SOLUTION:  As x increases by 1, y increases by 10. So, this is a linear function.

69. SCHOOLS A school district’s spending on students over the last five years is represented by the equation y =

325x2 + 0.2x + 1427. Is this equation linear? Explain.

SOLUTION:  

The equation y = 325x2 + 0.2x + 1427 represents a nonlinear function, because it cannot be written in the form y =

mx + b.

Graph each function.

70. y = 3x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x2 (x, y)

–2 y = 3(–2)2 = 12 (–2, 12)

–1 y = 3(–1)2 = 3 (–1, 3)

0 y = 3(0)2 = 0 (0, 0)

1 y = 3(1)2 = 3 (1, 3)

2 y = 3(2)2 = 12 (2, 12)

71. y = –2x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –2x2 (x, y)

–2 y = –2(–2)2 = –8 (–2, –8)

–1 y = –2(–1)2 = –2 (–1, –2)

0 y = –2(0)2 = 0 (0, 0)

1 y = –2(1)2 = –2 (1, –2)

2 y = –2(2)2 = –8 (2, –8)

72. y = x2 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x2 – 4 (x, y)

–2 y = (–2)2 – 4 = 0 (–2, 0)

–1 y = (–1)2 – 4 = –3 (–1, –3)

0 y = 02 – 4 = –4 (0, –4)

1 y = 12 – 4 = –3 (1, –3)

2 y = 22 – 4 = 0 (2, 0)

73. y = –x2 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –x2 + 1 (x, y)

–2 y = –(–2)2 + 1 = –3 (–2, –3)

–1 y = –(–1)2 + 1 = 0 (–1, 0)

0 y = –(0)2 + 1 = 1 (0, 1)

1 y = –(1)2 + 1 = 0 (1, 0)

2 y = –(2)2 + 1 = –3 (2, –3)

74. y = 2x2 + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x2 + 2 (x, y)

–2 y = 2(–2)2 + 2 = 10 (–2, 10)

–1 y = 2(–1)2 + 2 = 4 (–1, 4)

0 y = 2(0)2 + 2 = 2 (0, 2)

1 y = 2(1)2 + 2 = 4 (1, 4)

2 y = 2(2)2 + 2 = 10 (2, 10)

75. y = x2 – 3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x

2 – 3

(x, y)

–2 y = (–2)

2 – 3 = –1

(–2, –1)

–1 y = (–1)

2 – 3 = –2.5

(–1, –2.5)

0 y = (0)

2 – 3 = –3

(0, –3)

1 y = (1)

2 – 3 = –2.5

(1, –2.5)

2 y = (2)

2 – 3 = –1

(2, –1)

76. GEOMETRY The volume of a cylinder with a height of 8 inches can be found using the equation V = 8(3.14)r2

where r is the radius of the cylinder. Graph the equation.

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

r V = 8(3.14)r2 (r, V)

0 V = 8(3.14)(02) = 0 (0, 0)

1 V = 8(3.14)(12) = 25.12 (1, 25.12)

2 V = 8(3.14)(22) = 100.48 (2, 100.48)

3 V = 8(3.14)(32) = 226.08 (3, 226.08)

4 V = 8(3.14)(42) = 401.92 (4, 401.92)

Graph each function.

77. y = x3 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 + 1 (x, y)

–2 y = (–2)3 + 1 = –7 (–2, –7)

–1 y = (–1)3 + 1 = 0 (–1, 0)

0 y = 03 + 1 = 1 (0, 1)

1 y = 13 + 1 = 2 (1, 2)

2 y = 23 + 1 = 9 (2, 9)

78. y = –3x3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –3x3 (x, y)

–2 y = –3(–2)3 = 24 (–2, 24)

–1 y = –3(–1)3 = 3 (–1, 3)

0 y = –3(0)3 = 0 (0, 0)

1 y = –3(1)3 = –3 (1, –3)

2 y = –3(2)3 = –24 (2, –24)

79. y = x3 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 – 4 (x, y)

–2 y = (–2)3 – 4 = –12 (–2, –12)

–1 y = (–1)3 – 4 = –5 (–1, –5)

0 y = 03 – 4 = –4 (0, –4)

1 y = 13 – 4 = –3 (1, –3)

2 y = 23 – 4 = 4 (2, 4)

80. y = 2x + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x + 2 (x, y)

–2 y = 2–2

+ 2 = 2.25 (–2, 2.25)

–1 y = 2–1

+ 2 = 2.5 (–1, 2.5)

0 y = 20+ 2 = 3 (0, 3)

1 y = 21 + 2 = 4 (1, 4)

2 y = 22 + 2 = 6 (2, 6)

81. y = 3x

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x (x, y)

–2 y = 3

–2 =

(–2, )

–1 y = 3

–1 =

(–1, )

0 y = 30 = 1 (0, 1)

1 y = 31 = 3 (1, 3)

2 y = 32 = 9 (2, 9)

82. y = 2x – 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x – 1 (x, y)

–2 y = 2–2

– 1 = –0.75 (–2, –0.75)

–1 y = 2–1

– 1 = –0.5 (–1, –0.5)

0 y = 20 – 1 = 0 (0, 0)

1 y = 21 – 1 = 1 (1, 1)

2 y = 22 – 1 = 3 (2, 3)

83. LIFE SCIENCE Starting from a single bacterium in a dish, the number of bacteria after t cycles of reproduction is

2t. A bacterium reproduces every 30 minutes. If there are 1000 bacteria in a dish now, how many will there be in 1

hour?

SOLUTION:  

To find the number of bacteria will be in the dish in 1 hour, replace t with 2 in the expression 2t because there are 2

thirty minute cycles in 2 hour. Then, multiply the result by 1000 because there are 1000 bacteria in the dish now.

So, there will be 4000 bacteria in the dish in 1 hour.

eSolutions Manual - Powered by Cognero Page 17

Study Guide and Review

Determine whether each statement is true or false . If false , replace the underlined word or number to make a true statement.

1. The exponent of a number raised to the first power can be omitted.

SOLUTION:  An exponent tells how many times a number is used as a factor. So, the exponent of a number raised to the first power can be omitted. The statement is true.

2. A number is in scientific notation when it does not contain exponents.

SOLUTION:  A number that is expressed as a product of a factor and a power of 10 is written in scientific notation. So, the statement is false. A number is in standard form when it does not contain exponents.

3. In 57, the number 7 is the base.

SOLUTION:  

The number that is multiplied is called the base. So, the statement is false. In 57, the number 7 is the exponent.

4. The number 49 is an example of a(n) prime number.

SOLUTION:  A prime number is a whole number that has exactly two unique factors, 1 and itself. So, the statement is false. The number 49 is an example of a composite number.

5. The equation y = 5x + 2 is an example of a(n) exponential function.

SOLUTION:  

An exponential function is a function that can be described by an equation of the form y = ax + c, where a ≠ 0 and 

a ≠ 1. So, the statement is true.

6. The graph of a(n) cubic function is called a parabola.

SOLUTION:  The statement is false. The graph of a quadratic function is called a parabola.

7. To multiply powers with the same base, add the exponents.

SOLUTION:  The statement is true.

8. A(n) nonlinear function has a constant rate of change.

SOLUTION:  Nonlinear functions do not have constant rates of change. So, the statement is false. A linear function has a constant rate of change.

9. To simplify (n6)5, the first step is to add 6 and 5.

SOLUTION:  

To find the power of a power, multiply exponents. So, the statement is false. To simplify (n6)5, the first step is to

multiply 6 and 5.

10. The graph of a(n) quadratic function is symmetric.

SOLUTION:  The graph of a quadratic function is a parabola, which is symmetric. So, the statement is true.

Write each expression using exponents.11. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

12. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

13. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

14. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

15. 35

SOLUTION:  

16. 2 • 43

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

17. x2 – 6

SOLUTION:  

18. w3 + y2

SOLUTION:  

19. 2(y + z3)

SOLUTION:  

20. w4x

2yz

SOLUTION:  

21. TEETH Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

Write the prime factorization of each number. Use exponents for repeated factors.22. 34

SOLUTION:  34 = 2 • 17

23. 40

SOLUTION:  

24. 63

SOLUTION:  

25. 225

SOLUTION:  

Factor each monomial.26. 18x

SOLUTION:  18x = 2 • 3 • 3 • x

27. 10r2

SOLUTION:  

28. 32pq

SOLUTION:  32pq = 2 • 2 • 2 • 2 • 2 • p • q

29. –25ab2

SOLUTION:  

30. PHOTOGRAPHS Jacy has 24 photographs to put in a rectangular arrangement. In how many different numbers of rows and columns can she display them if each row has the same number of photographs? Name each arrangement.

SOLUTION:  List the different numbers of rows and columns by listing the factors of 24. So, Jacy could form rectangles with the following number of rows and columns: 1 • 24, 24 • 1, 2 • 12, 12 • 2, 3 • 8, 8 • 3, 4 • 6, 6 • 4. There are 8 different arrangements.

Find each product or quotient. Express using exponents.

31. 35 • 3

2

SOLUTION:  

32. (–7) • (–7)4

SOLUTION:  

33. m3 • m6

SOLUTION:  

34. x8 • x

SOLUTION:  

35. (2h7)(6h)

SOLUTION:  

36. (5a3)(–6a

4)

SOLUTION:  

37. 

SOLUTION:  

38. 

SOLUTION:  

39. PLANETS Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how

many times farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by thedistance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Write each expression using a positive exponent.

40. 9–4

SOLUTION:  

9–4

=

41. (–10)–2

SOLUTION:  

(–10)–2

=

42. m–5

SOLUTION:  

m–5 =

Write each fraction as an expression using a negative exponent other than –1.

43. 

SOLUTION:  

= 6–3

44. 

SOLUTION:  

or  or 

45. 

SOLUTION:  

46. MEASUREMENT If 1 millimeter is equal to 10–3

meter and 1 nanometer is equal to 10–9

meter, how many nanometers are in 1 millimeter? Write using a positive exponent.

SOLUTION:  To find the number of nanometers in 1 millimeter, divide the number of millimeters in a meter by the number of nanometers in a meter.

So, there are 106 nanometers in 1 millimeter.

Express each number in standard form.

47. 5.82 × 103

SOLUTION:  

48. 9.0 × 10–2

SOLUTION:  

49. 3.4 × 10–4

SOLUTION:  

50. 1.705 × 105

SOLUTION:  

Express each number in scientific notation.51. 379

SOLUTION:  

52. 26,880

SOLUTION:  

53. 0.0014

SOLUTION:  

54. 0.000561

SOLUTION:  

55. SPACE The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Simplify.

56. (26)3

SOLUTION:  

57. (r2)8

SOLUTION:  

58. (3x7)2

SOLUTION:  

59. (–2n4)6

SOLUTION:  

60. (4a9b)

4

SOLUTION:  

61. (5w5x

8)3

SOLUTION:  

62. GEOMETRY Find the area of the square shown below.

SOLUTION:  

Determine whether each graph, equation, or table represents a linear or nonlinear function. Explain.

63. 

SOLUTION:  The graph is a curve, not a straight line. So, it represents a nonlinear function.

64. 

SOLUTION:  The graph is a line. So, it represents a linear function.

65. y = x

SOLUTION:  

The equation y = x represents a linear function, because it is written in the form y = mx + b.

66. y =  + 1

SOLUTION:  

The equation y =  + 1 represents a nonlinear function, because it cannot be written in the form y = mx + b.

67. 

SOLUTION:  As x increases by 1, y decreases by 2. So, this is a linear function.

68. 

SOLUTION:  As x increases by 1, y increases by 10. So, this is a linear function.

69. SCHOOLS A school district’s spending on students over the last five years is represented by the equation y =

325x2 + 0.2x + 1427. Is this equation linear? Explain.

SOLUTION:  

The equation y = 325x2 + 0.2x + 1427 represents a nonlinear function, because it cannot be written in the form y =

mx + b.

Graph each function.

70. y = 3x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x2 (x, y)

–2 y = 3(–2)2 = 12 (–2, 12)

–1 y = 3(–1)2 = 3 (–1, 3)

0 y = 3(0)2 = 0 (0, 0)

1 y = 3(1)2 = 3 (1, 3)

2 y = 3(2)2 = 12 (2, 12)

71. y = –2x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –2x2 (x, y)

–2 y = –2(–2)2 = –8 (–2, –8)

–1 y = –2(–1)2 = –2 (–1, –2)

0 y = –2(0)2 = 0 (0, 0)

1 y = –2(1)2 = –2 (1, –2)

2 y = –2(2)2 = –8 (2, –8)

72. y = x2 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x2 – 4 (x, y)

–2 y = (–2)2 – 4 = 0 (–2, 0)

–1 y = (–1)2 – 4 = –3 (–1, –3)

0 y = 02 – 4 = –4 (0, –4)

1 y = 12 – 4 = –3 (1, –3)

2 y = 22 – 4 = 0 (2, 0)

73. y = –x2 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –x2 + 1 (x, y)

–2 y = –(–2)2 + 1 = –3 (–2, –3)

–1 y = –(–1)2 + 1 = 0 (–1, 0)

0 y = –(0)2 + 1 = 1 (0, 1)

1 y = –(1)2 + 1 = 0 (1, 0)

2 y = –(2)2 + 1 = –3 (2, –3)

74. y = 2x2 + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x2 + 2 (x, y)

–2 y = 2(–2)2 + 2 = 10 (–2, 10)

–1 y = 2(–1)2 + 2 = 4 (–1, 4)

0 y = 2(0)2 + 2 = 2 (0, 2)

1 y = 2(1)2 + 2 = 4 (1, 4)

2 y = 2(2)2 + 2 = 10 (2, 10)

75. y = x2 – 3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x

2 – 3

(x, y)

–2 y = (–2)

2 – 3 = –1

(–2, –1)

–1 y = (–1)

2 – 3 = –2.5

(–1, –2.5)

0 y = (0)

2 – 3 = –3

(0, –3)

1 y = (1)

2 – 3 = –2.5

(1, –2.5)

2 y = (2)

2 – 3 = –1

(2, –1)

76. GEOMETRY The volume of a cylinder with a height of 8 inches can be found using the equation V = 8(3.14)r2

where r is the radius of the cylinder. Graph the equation.

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

r V = 8(3.14)r2 (r, V)

0 V = 8(3.14)(02) = 0 (0, 0)

1 V = 8(3.14)(12) = 25.12 (1, 25.12)

2 V = 8(3.14)(22) = 100.48 (2, 100.48)

3 V = 8(3.14)(32) = 226.08 (3, 226.08)

4 V = 8(3.14)(42) = 401.92 (4, 401.92)

Graph each function.

77. y = x3 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 + 1 (x, y)

–2 y = (–2)3 + 1 = –7 (–2, –7)

–1 y = (–1)3 + 1 = 0 (–1, 0)

0 y = 03 + 1 = 1 (0, 1)

1 y = 13 + 1 = 2 (1, 2)

2 y = 23 + 1 = 9 (2, 9)

78. y = –3x3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –3x3 (x, y)

–2 y = –3(–2)3 = 24 (–2, 24)

–1 y = –3(–1)3 = 3 (–1, 3)

0 y = –3(0)3 = 0 (0, 0)

1 y = –3(1)3 = –3 (1, –3)

2 y = –3(2)3 = –24 (2, –24)

79. y = x3 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 – 4 (x, y)

–2 y = (–2)3 – 4 = –12 (–2, –12)

–1 y = (–1)3 – 4 = –5 (–1, –5)

0 y = 03 – 4 = –4 (0, –4)

1 y = 13 – 4 = –3 (1, –3)

2 y = 23 – 4 = 4 (2, 4)

80. y = 2x + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x + 2 (x, y)

–2 y = 2–2

+ 2 = 2.25 (–2, 2.25)

–1 y = 2–1

+ 2 = 2.5 (–1, 2.5)

0 y = 20+ 2 = 3 (0, 3)

1 y = 21 + 2 = 4 (1, 4)

2 y = 22 + 2 = 6 (2, 6)

81. y = 3x

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x (x, y)

–2 y = 3

–2 =

(–2, )

–1 y = 3

–1 =

(–1, )

0 y = 30 = 1 (0, 1)

1 y = 31 = 3 (1, 3)

2 y = 32 = 9 (2, 9)

82. y = 2x – 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x – 1 (x, y)

–2 y = 2–2

– 1 = –0.75 (–2, –0.75)

–1 y = 2–1

– 1 = –0.5 (–1, –0.5)

0 y = 20 – 1 = 0 (0, 0)

1 y = 21 – 1 = 1 (1, 1)

2 y = 22 – 1 = 3 (2, 3)

83. LIFE SCIENCE Starting from a single bacterium in a dish, the number of bacteria after t cycles of reproduction is

2t. A bacterium reproduces every 30 minutes. If there are 1000 bacteria in a dish now, how many will there be in 1

hour?

SOLUTION:  

To find the number of bacteria will be in the dish in 1 hour, replace t with 2 in the expression 2t because there are 2

thirty minute cycles in 2 hour. Then, multiply the result by 1000 because there are 1000 bacteria in the dish now.

So, there will be 4000 bacteria in the dish in 1 hour.

eSolutions Manual - Powered by Cognero Page 18

Study Guide and Review

Determine whether each statement is true or false . If false , replace the underlined word or number to make a true statement.

1. The exponent of a number raised to the first power can be omitted.

SOLUTION:  An exponent tells how many times a number is used as a factor. So, the exponent of a number raised to the first power can be omitted. The statement is true.

2. A number is in scientific notation when it does not contain exponents.

SOLUTION:  A number that is expressed as a product of a factor and a power of 10 is written in scientific notation. So, the statement is false. A number is in standard form when it does not contain exponents.

3. In 57, the number 7 is the base.

SOLUTION:  

The number that is multiplied is called the base. So, the statement is false. In 57, the number 7 is the exponent.

4. The number 49 is an example of a(n) prime number.

SOLUTION:  A prime number is a whole number that has exactly two unique factors, 1 and itself. So, the statement is false. The number 49 is an example of a composite number.

5. The equation y = 5x + 2 is an example of a(n) exponential function.

SOLUTION:  

An exponential function is a function that can be described by an equation of the form y = ax + c, where a ≠ 0 and 

a ≠ 1. So, the statement is true.

6. The graph of a(n) cubic function is called a parabola.

SOLUTION:  The statement is false. The graph of a quadratic function is called a parabola.

7. To multiply powers with the same base, add the exponents.

SOLUTION:  The statement is true.

8. A(n) nonlinear function has a constant rate of change.

SOLUTION:  Nonlinear functions do not have constant rates of change. So, the statement is false. A linear function has a constant rate of change.

9. To simplify (n6)5, the first step is to add 6 and 5.

SOLUTION:  

To find the power of a power, multiply exponents. So, the statement is false. To simplify (n6)5, the first step is to

multiply 6 and 5.

10. The graph of a(n) quadratic function is symmetric.

SOLUTION:  The graph of a quadratic function is a parabola, which is symmetric. So, the statement is true.

Write each expression using exponents.11. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

12. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

13. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

14. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

15. 35

SOLUTION:  

16. 2 • 43

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

17. x2 – 6

SOLUTION:  

18. w3 + y2

SOLUTION:  

19. 2(y + z3)

SOLUTION:  

20. w4x

2yz

SOLUTION:  

21. TEETH Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

Write the prime factorization of each number. Use exponents for repeated factors.22. 34

SOLUTION:  34 = 2 • 17

23. 40

SOLUTION:  

24. 63

SOLUTION:  

25. 225

SOLUTION:  

Factor each monomial.26. 18x

SOLUTION:  18x = 2 • 3 • 3 • x

27. 10r2

SOLUTION:  

28. 32pq

SOLUTION:  32pq = 2 • 2 • 2 • 2 • 2 • p • q

29. –25ab2

SOLUTION:  

30. PHOTOGRAPHS Jacy has 24 photographs to put in a rectangular arrangement. In how many different numbers of rows and columns can she display them if each row has the same number of photographs? Name each arrangement.

SOLUTION:  List the different numbers of rows and columns by listing the factors of 24. So, Jacy could form rectangles with the following number of rows and columns: 1 • 24, 24 • 1, 2 • 12, 12 • 2, 3 • 8, 8 • 3, 4 • 6, 6 • 4. There are 8 different arrangements.

Find each product or quotient. Express using exponents.

31. 35 • 3

2

SOLUTION:  

32. (–7) • (–7)4

SOLUTION:  

33. m3 • m6

SOLUTION:  

34. x8 • x

SOLUTION:  

35. (2h7)(6h)

SOLUTION:  

36. (5a3)(–6a

4)

SOLUTION:  

37. 

SOLUTION:  

38. 

SOLUTION:  

39. PLANETS Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how

many times farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by thedistance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Write each expression using a positive exponent.

40. 9–4

SOLUTION:  

9–4

=

41. (–10)–2

SOLUTION:  

(–10)–2

=

42. m–5

SOLUTION:  

m–5 =

Write each fraction as an expression using a negative exponent other than –1.

43. 

SOLUTION:  

= 6–3

44. 

SOLUTION:  

or  or 

45. 

SOLUTION:  

46. MEASUREMENT If 1 millimeter is equal to 10–3

meter and 1 nanometer is equal to 10–9

meter, how many nanometers are in 1 millimeter? Write using a positive exponent.

SOLUTION:  To find the number of nanometers in 1 millimeter, divide the number of millimeters in a meter by the number of nanometers in a meter.

So, there are 106 nanometers in 1 millimeter.

Express each number in standard form.

47. 5.82 × 103

SOLUTION:  

48. 9.0 × 10–2

SOLUTION:  

49. 3.4 × 10–4

SOLUTION:  

50. 1.705 × 105

SOLUTION:  

Express each number in scientific notation.51. 379

SOLUTION:  

52. 26,880

SOLUTION:  

53. 0.0014

SOLUTION:  

54. 0.000561

SOLUTION:  

55. SPACE The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Simplify.

56. (26)3

SOLUTION:  

57. (r2)8

SOLUTION:  

58. (3x7)2

SOLUTION:  

59. (–2n4)6

SOLUTION:  

60. (4a9b)

4

SOLUTION:  

61. (5w5x

8)3

SOLUTION:  

62. GEOMETRY Find the area of the square shown below.

SOLUTION:  

Determine whether each graph, equation, or table represents a linear or nonlinear function. Explain.

63. 

SOLUTION:  The graph is a curve, not a straight line. So, it represents a nonlinear function.

64. 

SOLUTION:  The graph is a line. So, it represents a linear function.

65. y = x

SOLUTION:  

The equation y = x represents a linear function, because it is written in the form y = mx + b.

66. y =  + 1

SOLUTION:  

The equation y =  + 1 represents a nonlinear function, because it cannot be written in the form y = mx + b.

67. 

SOLUTION:  As x increases by 1, y decreases by 2. So, this is a linear function.

68. 

SOLUTION:  As x increases by 1, y increases by 10. So, this is a linear function.

69. SCHOOLS A school district’s spending on students over the last five years is represented by the equation y =

325x2 + 0.2x + 1427. Is this equation linear? Explain.

SOLUTION:  

The equation y = 325x2 + 0.2x + 1427 represents a nonlinear function, because it cannot be written in the form y =

mx + b.

Graph each function.

70. y = 3x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x2 (x, y)

–2 y = 3(–2)2 = 12 (–2, 12)

–1 y = 3(–1)2 = 3 (–1, 3)

0 y = 3(0)2 = 0 (0, 0)

1 y = 3(1)2 = 3 (1, 3)

2 y = 3(2)2 = 12 (2, 12)

71. y = –2x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –2x2 (x, y)

–2 y = –2(–2)2 = –8 (–2, –8)

–1 y = –2(–1)2 = –2 (–1, –2)

0 y = –2(0)2 = 0 (0, 0)

1 y = –2(1)2 = –2 (1, –2)

2 y = –2(2)2 = –8 (2, –8)

72. y = x2 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x2 – 4 (x, y)

–2 y = (–2)2 – 4 = 0 (–2, 0)

–1 y = (–1)2 – 4 = –3 (–1, –3)

0 y = 02 – 4 = –4 (0, –4)

1 y = 12 – 4 = –3 (1, –3)

2 y = 22 – 4 = 0 (2, 0)

73. y = –x2 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –x2 + 1 (x, y)

–2 y = –(–2)2 + 1 = –3 (–2, –3)

–1 y = –(–1)2 + 1 = 0 (–1, 0)

0 y = –(0)2 + 1 = 1 (0, 1)

1 y = –(1)2 + 1 = 0 (1, 0)

2 y = –(2)2 + 1 = –3 (2, –3)

74. y = 2x2 + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x2 + 2 (x, y)

–2 y = 2(–2)2 + 2 = 10 (–2, 10)

–1 y = 2(–1)2 + 2 = 4 (–1, 4)

0 y = 2(0)2 + 2 = 2 (0, 2)

1 y = 2(1)2 + 2 = 4 (1, 4)

2 y = 2(2)2 + 2 = 10 (2, 10)

75. y = x2 – 3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x

2 – 3

(x, y)

–2 y = (–2)

2 – 3 = –1

(–2, –1)

–1 y = (–1)

2 – 3 = –2.5

(–1, –2.5)

0 y = (0)

2 – 3 = –3

(0, –3)

1 y = (1)

2 – 3 = –2.5

(1, –2.5)

2 y = (2)

2 – 3 = –1

(2, –1)

76. GEOMETRY The volume of a cylinder with a height of 8 inches can be found using the equation V = 8(3.14)r2

where r is the radius of the cylinder. Graph the equation.

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

r V = 8(3.14)r2 (r, V)

0 V = 8(3.14)(02) = 0 (0, 0)

1 V = 8(3.14)(12) = 25.12 (1, 25.12)

2 V = 8(3.14)(22) = 100.48 (2, 100.48)

3 V = 8(3.14)(32) = 226.08 (3, 226.08)

4 V = 8(3.14)(42) = 401.92 (4, 401.92)

Graph each function.

77. y = x3 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 + 1 (x, y)

–2 y = (–2)3 + 1 = –7 (–2, –7)

–1 y = (–1)3 + 1 = 0 (–1, 0)

0 y = 03 + 1 = 1 (0, 1)

1 y = 13 + 1 = 2 (1, 2)

2 y = 23 + 1 = 9 (2, 9)

78. y = –3x3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –3x3 (x, y)

–2 y = –3(–2)3 = 24 (–2, 24)

–1 y = –3(–1)3 = 3 (–1, 3)

0 y = –3(0)3 = 0 (0, 0)

1 y = –3(1)3 = –3 (1, –3)

2 y = –3(2)3 = –24 (2, –24)

79. y = x3 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 – 4 (x, y)

–2 y = (–2)3 – 4 = –12 (–2, –12)

–1 y = (–1)3 – 4 = –5 (–1, –5)

0 y = 03 – 4 = –4 (0, –4)

1 y = 13 – 4 = –3 (1, –3)

2 y = 23 – 4 = 4 (2, 4)

80. y = 2x + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x + 2 (x, y)

–2 y = 2–2

+ 2 = 2.25 (–2, 2.25)

–1 y = 2–1

+ 2 = 2.5 (–1, 2.5)

0 y = 20+ 2 = 3 (0, 3)

1 y = 21 + 2 = 4 (1, 4)

2 y = 22 + 2 = 6 (2, 6)

81. y = 3x

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x (x, y)

–2 y = 3

–2 =

(–2, )

–1 y = 3

–1 =

(–1, )

0 y = 30 = 1 (0, 1)

1 y = 31 = 3 (1, 3)

2 y = 32 = 9 (2, 9)

82. y = 2x – 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x – 1 (x, y)

–2 y = 2–2

– 1 = –0.75 (–2, –0.75)

–1 y = 2–1

– 1 = –0.5 (–1, –0.5)

0 y = 20 – 1 = 0 (0, 0)

1 y = 21 – 1 = 1 (1, 1)

2 y = 22 – 1 = 3 (2, 3)

83. LIFE SCIENCE Starting from a single bacterium in a dish, the number of bacteria after t cycles of reproduction is

2t. A bacterium reproduces every 30 minutes. If there are 1000 bacteria in a dish now, how many will there be in 1

hour?

SOLUTION:  

To find the number of bacteria will be in the dish in 1 hour, replace t with 2 in the expression 2t because there are 2

thirty minute cycles in 2 hour. Then, multiply the result by 1000 because there are 1000 bacteria in the dish now.

So, there will be 4000 bacteria in the dish in 1 hour.

eSolutions Manual - Powered by Cognero Page 19

Study Guide and Review

Determine whether each statement is true or false . If false , replace the underlined word or number to make a true statement.

1. The exponent of a number raised to the first power can be omitted.

SOLUTION:  An exponent tells how many times a number is used as a factor. So, the exponent of a number raised to the first power can be omitted. The statement is true.

2. A number is in scientific notation when it does not contain exponents.

SOLUTION:  A number that is expressed as a product of a factor and a power of 10 is written in scientific notation. So, the statement is false. A number is in standard form when it does not contain exponents.

3. In 57, the number 7 is the base.

SOLUTION:  

The number that is multiplied is called the base. So, the statement is false. In 57, the number 7 is the exponent.

4. The number 49 is an example of a(n) prime number.

SOLUTION:  A prime number is a whole number that has exactly two unique factors, 1 and itself. So, the statement is false. The number 49 is an example of a composite number.

5. The equation y = 5x + 2 is an example of a(n) exponential function.

SOLUTION:  

An exponential function is a function that can be described by an equation of the form y = ax + c, where a ≠ 0 and 

a ≠ 1. So, the statement is true.

6. The graph of a(n) cubic function is called a parabola.

SOLUTION:  The statement is false. The graph of a quadratic function is called a parabola.

7. To multiply powers with the same base, add the exponents.

SOLUTION:  The statement is true.

8. A(n) nonlinear function has a constant rate of change.

SOLUTION:  Nonlinear functions do not have constant rates of change. So, the statement is false. A linear function has a constant rate of change.

9. To simplify (n6)5, the first step is to add 6 and 5.

SOLUTION:  

To find the power of a power, multiply exponents. So, the statement is false. To simplify (n6)5, the first step is to

multiply 6 and 5.

10. The graph of a(n) quadratic function is symmetric.

SOLUTION:  The graph of a quadratic function is a parabola, which is symmetric. So, the statement is true.

Write each expression using exponents.11. 6 • 6 • 6 • 6 • 6

SOLUTION:  The base 6 is a factor 5 times. So, the exponent is 5.

6 • 6 • 6 • 6 • 6 = 65

12. 4

SOLUTION:  The base 4 is a factor 1 time. So, the exponent is 1.

4 = 41

13. x • x • x

SOLUTION:  The base x is a factor 3 times. So the exponent is 3.

x • x • x = x3

14. f • f • g • g • g • g

SOLUTION:  

Evaluate each expression.

15. 35

SOLUTION:  

16. 2 • 43

SOLUTION:  

Evaluate each expression if w = , x = 4, y = 1, and z = –5.

17. x2 – 6

SOLUTION:  

18. w3 + y2

SOLUTION:  

19. 2(y + z3)

SOLUTION:  

20. w4x

2yz

SOLUTION:  

21. TEETH Adult humans have 25 teeth. How many teeth do adults have?

SOLUTION:  

So, adult humans have 32 teeth.

Write the prime factorization of each number. Use exponents for repeated factors.22. 34

SOLUTION:  34 = 2 • 17

23. 40

SOLUTION:  

24. 63

SOLUTION:  

25. 225

SOLUTION:  

Factor each monomial.26. 18x

SOLUTION:  18x = 2 • 3 • 3 • x

27. 10r2

SOLUTION:  

28. 32pq

SOLUTION:  32pq = 2 • 2 • 2 • 2 • 2 • p • q

29. –25ab2

SOLUTION:  

30. PHOTOGRAPHS Jacy has 24 photographs to put in a rectangular arrangement. In how many different numbers of rows and columns can she display them if each row has the same number of photographs? Name each arrangement.

SOLUTION:  List the different numbers of rows and columns by listing the factors of 24. So, Jacy could form rectangles with the following number of rows and columns: 1 • 24, 24 • 1, 2 • 12, 12 • 2, 3 • 8, 8 • 3, 4 • 6, 6 • 4. There are 8 different arrangements.

Find each product or quotient. Express using exponents.

31. 35 • 3

2

SOLUTION:  

32. (–7) • (–7)4

SOLUTION:  

33. m3 • m6

SOLUTION:  

34. x8 • x

SOLUTION:  

35. (2h7)(6h)

SOLUTION:  

36. (5a3)(–6a

4)

SOLUTION:  

37. 

SOLUTION:  

38. 

SOLUTION:  

39. PLANETS Venus is about 108 kilometers from the Sun. Saturn is about 10

9 kilometers from the Sun. About how

many times farther from the Sun is Saturn than Venus?

SOLUTION:  To find how many times farther from the Sun Saturn is than Venus, divide the distance Saturn is from the sun by thedistance Venus is from the Sun.

So, Saturn is about 10 times further from the Sun than Venus.

Write each expression using a positive exponent.

40. 9–4

SOLUTION:  

9–4

=

41. (–10)–2

SOLUTION:  

(–10)–2

=

42. m–5

SOLUTION:  

m–5 =

Write each fraction as an expression using a negative exponent other than –1.

43. 

SOLUTION:  

= 6–3

44. 

SOLUTION:  

or  or 

45. 

SOLUTION:  

46. MEASUREMENT If 1 millimeter is equal to 10–3

meter and 1 nanometer is equal to 10–9

meter, how many nanometers are in 1 millimeter? Write using a positive exponent.

SOLUTION:  To find the number of nanometers in 1 millimeter, divide the number of millimeters in a meter by the number of nanometers in a meter.

So, there are 106 nanometers in 1 millimeter.

Express each number in standard form.

47. 5.82 × 103

SOLUTION:  

48. 9.0 × 10–2

SOLUTION:  

49. 3.4 × 10–4

SOLUTION:  

50. 1.705 × 105

SOLUTION:  

Express each number in scientific notation.51. 379

SOLUTION:  

52. 26,880

SOLUTION:  

53. 0.0014

SOLUTION:  

54. 0.000561

SOLUTION:  

55. SPACE The mass of the Sun is 1.98892 × 1015

exagrams. Express in standard form.

SOLUTION:  

So, the mass of the Sun is 1,988,920,000,000,000 exagrams.

Simplify.

56. (26)3

SOLUTION:  

57. (r2)8

SOLUTION:  

58. (3x7)2

SOLUTION:  

59. (–2n4)6

SOLUTION:  

60. (4a9b)

4

SOLUTION:  

61. (5w5x

8)3

SOLUTION:  

62. GEOMETRY Find the area of the square shown below.

SOLUTION:  

Determine whether each graph, equation, or table represents a linear or nonlinear function. Explain.

63. 

SOLUTION:  The graph is a curve, not a straight line. So, it represents a nonlinear function.

64. 

SOLUTION:  The graph is a line. So, it represents a linear function.

65. y = x

SOLUTION:  

The equation y = x represents a linear function, because it is written in the form y = mx + b.

66. y =  + 1

SOLUTION:  

The equation y =  + 1 represents a nonlinear function, because it cannot be written in the form y = mx + b.

67. 

SOLUTION:  As x increases by 1, y decreases by 2. So, this is a linear function.

68. 

SOLUTION:  As x increases by 1, y increases by 10. So, this is a linear function.

69. SCHOOLS A school district’s spending on students over the last five years is represented by the equation y =

325x2 + 0.2x + 1427. Is this equation linear? Explain.

SOLUTION:  

The equation y = 325x2 + 0.2x + 1427 represents a nonlinear function, because it cannot be written in the form y =

mx + b.

Graph each function.

70. y = 3x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x2 (x, y)

–2 y = 3(–2)2 = 12 (–2, 12)

–1 y = 3(–1)2 = 3 (–1, 3)

0 y = 3(0)2 = 0 (0, 0)

1 y = 3(1)2 = 3 (1, 3)

2 y = 3(2)2 = 12 (2, 12)

71. y = –2x2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –2x2 (x, y)

–2 y = –2(–2)2 = –8 (–2, –8)

–1 y = –2(–1)2 = –2 (–1, –2)

0 y = –2(0)2 = 0 (0, 0)

1 y = –2(1)2 = –2 (1, –2)

2 y = –2(2)2 = –8 (2, –8)

72. y = x2 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x2 – 4 (x, y)

–2 y = (–2)2 – 4 = 0 (–2, 0)

–1 y = (–1)2 – 4 = –3 (–1, –3)

0 y = 02 – 4 = –4 (0, –4)

1 y = 12 – 4 = –3 (1, –3)

2 y = 22 – 4 = 0 (2, 0)

73. y = –x2 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –x2 + 1 (x, y)

–2 y = –(–2)2 + 1 = –3 (–2, –3)

–1 y = –(–1)2 + 1 = 0 (–1, 0)

0 y = –(0)2 + 1 = 1 (0, 1)

1 y = –(1)2 + 1 = 0 (1, 0)

2 y = –(2)2 + 1 = –3 (2, –3)

74. y = 2x2 + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x2 + 2 (x, y)

–2 y = 2(–2)2 + 2 = 10 (–2, 10)

–1 y = 2(–1)2 + 2 = 4 (–1, 4)

0 y = 2(0)2 + 2 = 2 (0, 2)

1 y = 2(1)2 + 2 = 4 (1, 4)

2 y = 2(2)2 + 2 = 10 (2, 10)

75. y = x2 – 3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x

2 – 3

(x, y)

–2 y = (–2)

2 – 3 = –1

(–2, –1)

–1 y = (–1)

2 – 3 = –2.5

(–1, –2.5)

0 y = (0)

2 – 3 = –3

(0, –3)

1 y = (1)

2 – 3 = –2.5

(1, –2.5)

2 y = (2)

2 – 3 = –1

(2, –1)

76. GEOMETRY The volume of a cylinder with a height of 8 inches can be found using the equation V = 8(3.14)r2

where r is the radius of the cylinder. Graph the equation.

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

r V = 8(3.14)r2 (r, V)

0 V = 8(3.14)(02) = 0 (0, 0)

1 V = 8(3.14)(12) = 25.12 (1, 25.12)

2 V = 8(3.14)(22) = 100.48 (2, 100.48)

3 V = 8(3.14)(32) = 226.08 (3, 226.08)

4 V = 8(3.14)(42) = 401.92 (4, 401.92)

Graph each function.

77. y = x3 + 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 + 1 (x, y)

–2 y = (–2)3 + 1 = –7 (–2, –7)

–1 y = (–1)3 + 1 = 0 (–1, 0)

0 y = 03 + 1 = 1 (0, 1)

1 y = 13 + 1 = 2 (1, 2)

2 y = 23 + 1 = 9 (2, 9)

78. y = –3x3

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = –3x3 (x, y)

–2 y = –3(–2)3 = 24 (–2, 24)

–1 y = –3(–1)3 = 3 (–1, 3)

0 y = –3(0)3 = 0 (0, 0)

1 y = –3(1)3 = –3 (1, –3)

2 y = –3(2)3 = –24 (2, –24)

79. y = x3 – 4

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = x3 – 4 (x, y)

–2 y = (–2)3 – 4 = –12 (–2, –12)

–1 y = (–1)3 – 4 = –5 (–1, –5)

0 y = 03 – 4 = –4 (0, –4)

1 y = 13 – 4 = –3 (1, –3)

2 y = 23 – 4 = 4 (2, 4)

80. y = 2x + 2

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x + 2 (x, y)

–2 y = 2–2

+ 2 = 2.25 (–2, 2.25)

–1 y = 2–1

+ 2 = 2.5 (–1, 2.5)

0 y = 20+ 2 = 3 (0, 3)

1 y = 21 + 2 = 4 (1, 4)

2 y = 22 + 2 = 6 (2, 6)

81. y = 3x

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 3x (x, y)

–2 y = 3

–2 =

(–2, )

–1 y = 3

–1 =

(–1, )

0 y = 30 = 1 (0, 1)

1 y = 31 = 3 (1, 3)

2 y = 32 = 9 (2, 9)

82. y = 2x – 1

SOLUTION:  Make a table of values, plot the ordered pairs, and connect the points with a curve.

x y = 2x – 1 (x, y)

–2 y = 2–2

– 1 = –0.75 (–2, –0.75)

–1 y = 2–1

– 1 = –0.5 (–1, –0.5)

0 y = 20 – 1 = 0 (0, 0)

1 y = 21 – 1 = 1 (1, 1)

2 y = 22 – 1 = 3 (2, 3)

83. LIFE SCIENCE Starting from a single bacterium in a dish, the number of bacteria after t cycles of reproduction is

2t. A bacterium reproduces every 30 minutes. If there are 1000 bacteria in a dish now, how many will there be in 1

hour?

SOLUTION:  

To find the number of bacteria will be in the dish in 1 hour, replace t with 2 in the expression 2t because there are 2

thirty minute cycles in 2 hour. Then, multiply the result by 1000 because there are 1000 bacteria in the dish now.

So, there will be 4000 bacteria in the dish in 1 hour.

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