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Car
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295D Chapter 5 Exponential Functions
5
Warm Up
1. Write the first five terms of each sequence described and then identify the sequence as arithmetic or geometric.
a. The first term of the sequence is 23 and the common difference is 5.
b. The first term of the sequence is 23 and the common ratio is 5.
2. Write a function that describes the sequence in part (a) in explicit form.
3. Write a function that describes the sequence in part (b) in explicit form.
4. Which sequence in Question 1 is described by an exponential function?
5. Which sequence in Question 1 is described by a linear function?
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5.1 Comparing Linear and Exponential Functions 304A
5
Check for Students’ Understanding
Suppose that your family deposited $10,000 in an interest bearing account for your college fund that earns 4% simple interest each year and a friend’s family deposited $10,000 in an interest bearing account for their child’s college fund that earns 4% compound interest each year.
Use the simple and compound interest formulas to complete the table and round the values in the table to the nearest cent.
TimeSimple Interest
BalanceCompound Interest
Balance
Units
Expression
0
1
2
3
10
How much money will you and your friend have in the college funds when you each turn 18 years old?
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5.2 Graphs of Exponential Functions 305C
Warm Up
1. Describe the relationship between the two functions
f(x) 5 2x
f(x) 5 1 ? 2x
Use a graphing calculator to graph each exponential function.
2. f(x) 5 2x
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2222
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y
3. f(x) 5 2 ? 2x
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2222
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28
28
y
4. f(x) 5 3 ? 2x
x86
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8
2222
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28
28
y
5. f(x) 5 4 ? 2x
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2222
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28
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305D Chapter 5 Exponential Functions
5
6. Describe the graphical effect as the common ratio increases in the equation of the exponential function.
7. Without graphing the function, describe the graph of f(x) 5 5 ? 2x
8. Graph the function f(x) 5 5 ? 2x to verify your answer to Question 6.
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2222
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Car
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5.2 Graphs of Exponential Functions 312A
Check for Students’ Understanding
1. The deer population in a local neighborhood is rising at a rate of 3.5% each year. The parks and recreation department estimated the current deer population to be approximately 850 deer.
• Write the function, f(t), to represent the increase in the deer population as a function of time in years.
• Use the function to create a table of values.
• Use the table of values to graph the function.
• Use a graphing calculator to verify your graph.
xYears
f (x)Deer Population
2. In how many years will the deer population reach 1,000?
3. In how many years will the deer population reach 2,000?
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5.3 Translations of Linear and Exponential Functions 313C
Warm Up
1. Graph the function f(x) 5 x.
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2. Move every point on the graph of the function f(x) up 4 units and graph the new function, g(x).
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3. Write the function graphed in Question 2.
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313D Chapter 5 Exponential Functions
5
4. Move every point on the graph of the function g(x) to the right 4 units and graph the new function, h(x).
x86
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2222
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5. Write the function graphed in Question 4.
6. Describe the graphical effect of moving a linear function up 4 units and then to the right 4 units.
7. What do you think would be the graphical effect of moving a linear function down 4 units and then to the left 4 units.
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Car
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5.3 Translations of Linear and Exponential Functions 326A
Check for Students’ Understanding
Use a graphing calculator to graph each exponential function.
1. f(x) 5 2 ? 2 x
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2222
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2. f(x) 5 22 ? 2 x
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y
3. f(x) 5 2 ? 2 2x
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y
4. f(x) 5 22 ? 2 2x
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Car
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326B Chapter 5 Exponential Functions
5
Consider the function in Question 1 as the root function and compare it to the graphs in Questions 2 and 3.
5. Describe the graphical effect the negative sign has on the common ratio.
6. Describe the graphical effect the negative sign has on the exponent.
7. What do you predict the graph of the function f(x) 5 22 ? 2 2x will look like?
8. Graph the function f(x) 5 22 ? 2 2x to verify your answer to Question 7.
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2222
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Car
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5.4 Reflections of Linear and Exponential Functions 327C
Warm Up
1. Graph a linear function with a slope of 2.
x43
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2
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2121
21022
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y
2. Write an equation for the function graphed in Question 1.
3. Graph a linear function with a y-intercept at (0, 5)
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2222
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4. Write an equation for the function graphed in Question 3.
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Car
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327D Chapter 5 Exponential Functions
5
5. Graph a linear function with a slope of 2 and a y-intercept at (0, 5)
x43
1
2
3
4
2121
210222324
y
5
6
7
6. Write an equation for the function graphed in Question 5.
7. Describe the graph in Question 5 if it was translated down 5 units.
8. Describe the graph in Question 5 if it was translated to the right 2.5 units.
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5.4 Reflections of Linear and Exponential Functions 336A
Check for Students’ Understanding
1. Graph an increasing exponential function.
x86
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2. Write an equation for the function graphed in Question 1.
3. Perform a transformation on the function graphed in Question 1 to change it to a decreasing function.
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4. Write an equation for the function graphed in Question 3.
5. Describe the transformation performed on the function in Question 3.
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Car
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336B Chapter 5 Exponential Functions
5
6. Perform a transformation on the function graphed in Question 1 to shift it up 5 units.
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7. Write an equation for the function graphed in Question 6.
8. Describe the transformation performed on the function in Question 6
9. Perform a transformation on the function graphed in Question 1 to shift it to the right 5 units.
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10. Write an equation for the function graphed in Question 9.
11. Describe the transformation performed on the function in Question 9
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5.5 Properties of Rational Exponents 337C
Warm Up
Simplify each expression using the Quotient Rule of Powers.
1. x6 __
x2
2. x8 __
x3
3. 10x6 ____
5x2
4. 6x3 ___
9x5
5. xy10
____ x2y
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Car
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346 Chapter 5 Exponential Functions
5
Check for Students’ Understanding
Match each rational expression with the appropriate radical expression.
Rational Expression Radical Expression
1. 2 5 ___
10 A. 5 102
2. 10 5 __ 2
B. 5 210
3. 10 2 __ 5
C. 10 25
4. 5 10 ___ 2
D. 2 105
5. 2 10 ___ 5
E. 2 510
6. 5 2 ___
10 F. 10
52
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Car
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5.6 Solving Exponential Functions 347C
Warm Up
1. Complete the table by using an exponent with a base of 3 to express each term value.
Term Term ValueExponential Equivalent
1 1
2 3
3 9
4 27
5 81
6 243
2. What is the value of the 7th term?
3. How did you determine the value of the 7th term?
4. How would you determine the value of the 10th term?
5. How would you determine the value of the 100th term?
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Car
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5.6 Solving Exponential Functions 354A
Check for Students’ Understanding
Solve and explain each step.
4x 5 ( 1 __ 2 ) x 2 15
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