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

Chapter 8 – Exponential Functions Answer Key

CK-12 Algebra I Concepts 2

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

Chapter 8 – Exponential Functions Answer Key

CK-12 Algebra I Concepts 3

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

Chapter 8 – Exponential Functions Answer Key

CK-12 Algebra I Concepts 4

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

Chapter 8 – Exponential Functions Answer Key

CK-12 Algebra I Concepts 5

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

Chapter 8 – Exponential Functions Answer Key

CK-12 Algebra I Concepts 6

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

Chapter 8 – Exponential Functions Answer Key

CK-12 Algebra I Concepts 7

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

Chapter 8 – Exponential Functions Answer Key

CK-12 Algebra I Concepts 8

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

12. 9 significant digits

13. 3 significant digits

14. 7 significant digits

15. 3.0

16. 83

Chapter 8 – Exponential Functions Answer Key

CK-12 Algebra I Concepts 9

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

Chapter 8 – Exponential Functions Answer Key

CK-12 Algebra I Concepts 10

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

Chapter 8 – Exponential Functions Answer Key

CK-12 Algebra I Concepts 11

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

Chapter 8 – Exponential Functions Answer Key

CK-12 Algebra I Concepts 12

8.11 Graphs of Exponential Functions

Answers

1.

2.

3.

Chapter 8 – Exponential Functions Answer Key

CK-12 Algebra I Concepts 13

4.

5.

6.

Chapter 8 – Exponential Functions Answer Key

CK-12 Algebra I Concepts 14

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

Chapter 8 – Exponential Functions Answer Key

CK-12 Algebra I Concepts 15

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

Chapter 8 – Exponential Functions Answer Key

CK-12 Algebra I Concepts 16

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)