Chapter 8 Exponential Functions Answer Key

Chapter 8 – Exponential Functions Answer Key

CK-12 Algebra I Concepts 1

8.1 Exponential Properties Involving Products

Answers

1. 45

2. (3𝑥)3

3. (−2𝑎)4

4. 63𝑥2𝑦4

5. 23𝑥2𝑦2

6. 625

7. 64

8. 0.00001

9. -0.216

10. 126.44

11. 0.072

12. 10,077,696 or 69

13. 4096 or 212

14. 576 or 242

15. 𝑥6

16. 6𝑦5

17. 60𝑎7



8.2 Exponential Terms Raised to an Exponent

Answers

1. 𝑎12

2. 𝑥2𝑦2

3. −125𝑦3

4. 81𝑎8𝑏12

5. −32𝑥5𝑦20𝑧10

6. −12,800𝑥5

7. 𝑥5𝑦3

8. 64𝑎14

9. 1728𝑥3𝑦3

10. 6𝑥7𝑦6



8.3 Exponential Properties Involving Quotients

Answers

1. 54 = 625

2. 64 = 1296

3. 3−6 =1

729

4. 62

52 =36

25

5. 52

34 =25

81

6. 𝑎

7. 1

𝑥4

8. 𝑥4

𝑦3

9. 3𝑎

10. 3𝑥4

11. 5𝑥4

4𝑦4



8.4 Exponent of a Quotient

Answers

1. 9

64

2. 26

39 =64

19683

3. 44

22 = 64

4. 𝑎3𝑏6

5. 184𝑎16

154𝑎40 =184

154𝑎24

6. 𝑥6

𝑦6

7. 60𝑎3

16𝑏7

8. 3𝑎2𝑐4

9. 972

10. −27

11. 8

81

12. 0

13. 72𝑐

4



8.5 Negative Exponents

Answers

1. 𝑦2

𝑥

2. 1

𝑥4

3. 𝑥4

4. 𝑧7

𝑥3𝑦5

5. 𝑏2

𝑎2

6. 27𝑎−6𝑏6𝑐9

7. 𝑎4

8. 5𝑥−2𝑦

9. 64𝑎−2𝑏13

10. 3𝑥7𝑦−2

11. 𝑎−2𝑏−3𝑐



8.6 Fractional Exponents

Answers

1. 𝑥

52

𝑦13

2. 1

3. 1

4. 𝑥8

𝑦

5. √𝑥𝑦5

6. √𝑎3𝑏−34

7. 3𝑥𝑦

8. 𝑥−1𝑦

9. √𝑎−1 √𝑏−23

10. (𝑏

34

𝑎12

)

2

= √𝑏3𝑎−1



8.7 Evaluating Exponential Expressions

Answers

1. 1

9

2. −1

64

3. 1

4. 64

5. 64

6. 512

7. 16

8. 41

9. 272

252 =729

625

10. 1

12



8.8 Scientific Notation

Answers

1. 310.2

2. 74,000

3. 0.00175

4. 0.000029

5. 0.00000000999

6. 1.2 × 105

7. 1.765244 × 106

8. 1.2 × 101

9. 2.81 × 10−3

10. 2.7 × 10−8

11. 8 significant digits




15. 3.0

16. 83



8.9 Scientific Notation with a Calculator

Answers

1. 7.7 × 1011

2. 7 × 106

3. 3.72 × 10−8

4. 2 × 10−3

5. 4.8 × 1012

6. 6.6 × 10−4

7. 2.5 × 10−5

8. 5 × 1015

9. 3 × 10−8

10. 1.5 × 107 mi2

11. 9.6 × 104 coulombs

12. 6.8 × 108 miles per hour



8.10 Geometric Sequences and Exponential Functions

Answers

1. 2, 6, 18, 54, 162

2. 90, -30, 10, -3.34, 1.11

3. 6, -12, 24, -48, 96

4. 1, 5, 25, 125, 625

5. 5, 25, 125, 625, 3125

6. 25, 125, 625, 3125, 15625

7. Items 4, 5, and 6 are the same sequence

8. 3, 12, 48, 192, 768

9. 81, 27, 9, 3, 1

10. 9

4,

𝟑

𝟐, 𝟏,

2

3,

𝟒

𝟗

11. 2, –6, 18, –54, 162

12. 128

13. 𝑎4 = 2.95

14. 𝑎10 = 196830



15. 𝑟 = 2, 𝑎1 = 7

16. 𝑟 = √43

, 𝑎1 = 17.64 = (28

√43 )

17.

a. Answers will vary, but 𝑎1 = 1, 𝑎3 = 9, 𝑟 = 3 is common

b. Answers will vary, but 𝑎1 = 1, 𝑎2 = 9, 𝑟 = 9 is common

c. Answers will vary, but 𝑎1 = 6, 𝑎3 = 24, 𝑟 = 2 is common

d. Answers will vary, but 𝑎1 = 6, 𝑎2 = 24, 𝑟 = 4 is common

e. 𝑟 = 3

f. 𝑟 =1

3

g. The ratios are multiplicative inverses.

18. 𝑎3 = 43.2

a. 𝑎3 = 43.2 feet

b. 𝑎12 = 0.435 feet



8.11 Graphs of Exponential Functions

Answers

1.

2.

3.



4.

5.

6.



7.

8.

9. Graphs 1 and 7 are mirrored

10. 𝑦 = 3(10)−𝑥

11. 𝑦 = 5−𝑥

12. 𝑦 = 4 (3

2)

−𝑥

13.

a. 107 people

b. 97 people

14. $443.12



8.12 Applications of Exponential Functions

Answers

1. $443.12

2. $452.90

3. 425 people

4.

a. 80.65% remaining

b. 65.21% remaining

c. Answers will vary

d. Answers will vary. Correct time is apx. 19 ½ hrs.

5.

a. 1147 species remain

b. 1218 species in 1980

6. 343 stores on Jan. 1, 2007, or 370 on Dec 31, 2007

7.

a. $833.82

b. $653.53

c. Investment a

8.

a.

b. 𝑦 =. 82𝑥(7200)

c. $990



9.

a. 0.70

b. 100%

c. 1.3%

10.

a.

b. 𝑦 = 0.25𝑥(2000000)

c. Only 2 bacteria remain after 10 days

d. None remain (only actually requires 11 days)

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Chapter 8 Exponential Functions Answer Key