Upload
others
View
10
Download
0
Embed Size (px)
Citation preview
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)