answer key - mr. napper's webpage...answer key 3. f(n) 5 8 ? 2.5n y x 80,000 90,000 70,000...
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INTRODUCTION TO EXPONENTIAL FUNCTIONS: Skills Practice Answers • 1
I. A.1. f(n) 5 5 __ 2 ? 2n
y
x
24002700
21001800150012009006003000
2 3 4 5 6 7 81 9
2. f(n) 5 21 ? 3n
y
x–10,000–20,000–30,000–40,000–50,000–60,000–70,000–80,000
0 2 3 4 5 6 7 81 9
Answer Key
3. f(n) 5 8 ? 2.5n
y
x
80,00090,000
70,00060,00050,00040,00030,00020,00010,000
02 3 4 5 6 7 81 9
4. f(n) 5 1000 ? 0.9n
y
x
800900
7006005004003002001000
2 3 4 5 6 7 81 9
Module 3, Topic 1
INTRODUCTION TO EXPONENTIAL FUNCTIONS
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Module 3, Topic 1
INTRODUCTION TO EXPONENTIAL FUNCTIONS
5. f(n) 5 20.25 ? 2n
y
x–30–60–90–120–150–180–210–240
0 2 3 4 5 6 7 81 9
6. f(n) 5 1000 ? 1.25n
y
x
80009000
7000600050004000300020001000
02 3 4 5 6 7 81 9
2 • MODULE 3: Investigating Growth and Decay
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INTRODUCTION TO EXPONENTIAL FUNCTIONS: Skills Practice Answers • 3
Module 3, Topic 1
INTRODUCTION TO EXPONENTIAL FUNCTIONS
1.
x f(x)
22 1 __ 4
21 1 __ 2
0 1
1 2
2 4
constant ratio: 2 y-intercept: (0, 1)
2.
x f(x)
22 1 __ 16
21 1 __ 4
0 1
1 4
2 16
constant ratio: 4 y-intercept: (0, 1)
−4 −3 −2 −1−1
−2
10 2 3 4
−4
−3
4
3
2
1
y
x
−16 −12 −8 −4−4
−8
40 8 12 16
−16
−12
16
12
8
4
y
x
II. A.
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4 • MODULE 3: Investigating Growth and Decay
Module 3, Topic 1
INTRODUCTION TO EXPONENTIAL FUNCTIONS
3.
x f(x)
22 9
21 3
0 1
1 1 __ 3
2 1 __ 9
constant ratio: 1 __ 3 y-intercept: (0, 1)
4.
x f(x)
22 16
21 4
0 1
1 1 __ 4
2 1 __ 16
constant ratio: 1 __ 4 y-intercept: (0, 1)
−8 −6 −4 −2−2
−4
20 4 6 8
−8
−6
8
6
4
2
y
x
−16 −12 −8 −4−4
−8
40 8 12 16
−16
−12
16
12
8
4
y
x
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INTRODUCTION TO EXPONENTIAL FUNCTIONS: Skills Practice Answers • 5
Module 3, Topic 1
INTRODUCTION TO EXPONENTIAL FUNCTIONS
5.
x f(x)
22 2 1 __ 2
21 21
0 22
1 24
2 28
constant ratio: 2 y-intercept: (0, 22)
6.
x f(x)
22 28
21 24
0 22
1 21
2 2 1 __ 2
constant ratio: 1 __ 2 y-intercept: (0, 22)
−8 −6 −4 −2−2
−4
20 4 6 8
−8
−6
8
6
4
2
y
x
−8 −6 −4 −2−2
−4
20 4 6 8
−8
−6
8
6
4
2
y
x
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6 • MODULE 3: Investigating Growth and Decay
Module 3, Topic 1
INTRODUCTION TO EXPONENTIAL FUNCTIONS
7.
x f(x)
22 18
21 6
0 2
1 2 __ 3
2 2 __ 9
constant ratio: 1 __ 3 y-intercept: (0, 2)
8.
x f(x)
22 4
21 2
0 1
1 1 __ 2
2 1 __ 4
constant ratio: 1 __ 2 y-intercept: (0, 1)
−16 −12 −8 −4−4
−8
40 8 12 16
−16
−12
16
12
8
4
y
x
−4 −3 −2 −1−1
−2
10 2 3 4
−4
−3
4
3
2
1
y
x
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INTRODUCTION TO EXPONENTIAL FUNCTIONS: Skills Practice Answers • 7
Module 3, Topic 1
INTRODUCTION TO EXPONENTIAL FUNCTIONS
9.
x f(x)
22 2 1 __ 3
21 21
0 23
1 29
2 227
constant ratio: 3 y-intercept: (0, 23)
10.
x f(x)
22 2 1 __ 16
21 2 1 __ 4
0 21
1 24
2 216
constant ratio: 4 y-intercept: (0, 21)
−16 −12 −8 −4−4
−8
40 8 12 16
−16
−12
16
12
8
4
y
x
−16 −12 −8 −4−4
−8
40 8 12 16
−16
−12
16
12
8
4
y
x
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8 • MODULE 3: Investigating Growth and Decay
Module 3, Topic 1
INTRODUCTION TO EXPONENTIAL FUNCTIONS
11.
x f(x)
22 1 __ 2
21 1
0 2
1 4
2 8
constant ratio: 2 y-intercept: (0, 2)
12.
x f(x)
22 248
21 212
0 23
1 2 3 __ 4
2 2 3 __ 16
constant ratio: 1 __ 4 y-intercept: (0, 23)
−8 −6 −4 −2−2
−4
20 4 6 8
−8
−6
8
6
4
2
y
x
−16 −12 −8 −4−4
−8
40 8 12 16
−16
−12
16
12
8
4
y
x
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INTRODUCTION TO EXPONENTIAL FUNCTIONS: Skills Practice Answers • 9
Module 3, Topic 1
INTRODUCTION TO EXPONENTIAL FUNCTIONS
III. A.1. g(x) 5 2x 1 3
−8 −6 −4 −2−2
−4
20 4 6 8
−8
−6
8
6
4
2
y
x
2. g(x) 5 ( 1 __ 2 ) x 2 5
−8 −6 −4 −2−2
−4
20 4 6 8
−8
−6
8
6
4
2
y
x
3. g(x) 5 3x 2 1 2 2
−8 −6 −4 −2−2
−4
20 4 6 8
−8
−6
8
6
4
2
y
x
4. g(x) 5 2 ? ( 1 __ 3 ) x 2 4
−8 −6 −4 −2−2
−4
20 4 6 8
−8
−6
8
6
4
2
y
x
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10 • MODULE 3: Investigating Growth and Decay
Module 3, Topic 1
INTRODUCTION TO EXPONENTIAL FUNCTIONS
5. g(x) 5 4x 1 1
−8 −6 −4 −2−2
−4
20 4 6 8
−8
−6
8
6
4
2
y
x
6. g(x) 5 ( 2 __ 3 ) x 1 3
−8 −6 −4 −2−2
−4
20 4 6 8
−8
−6
8
6
4
2
y
x
7. g(x) 5 2x 2 1
−8 −6 −4 −2−2
−4
20 4 6 8
−8
−6
8
6
4
2
y
x
8. g(x) 5 ( 1 __ 2 ) x 1 4
−8 −6 −4 −2−2
−4
20 4 6 8
−8
−6
8
6
4
2
y
x
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INTRODUCTION TO EXPONENTIAL FUNCTIONS: Skills Practice Answers • 11
Module 3, Topic 1
INTRODUCTION TO EXPONENTIAL FUNCTIONS
9. g(x) 5 3x 2 2
−8 −6 −4 −2−2
−4
20 4 6 8
−8
−6
8
6
4
2
y
x
10. g(x) 5 ( 1 __ 4 ) x 1 5
−8 −6 −4 −2−2
−4
20 4 6 8
−8
−6
8
6
4
2
y
x
11. g(x) 5 ( 1 __ 3 ) x 2 3
−8 −6 −4 −2−2
−4
20 4 6 8
−8
−6
8
6
4
2
y
x
12. g(x) 5 4x 2 5
−8 −6 −4 −2−2
−4
20 4 6 8
−8
−6
8
6
4
2
y
x
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12 • MODULE 3: Investigating Growth and Decay
Module 3, Topic 1
INTRODUCTION TO EXPONENTIAL FUNCTIONS
13. g(x) 5 1 __ 2 ? 3x
−8 −6 −4 −2−2
−4
20 4 6 8
−8
−6
8
6
4
2
y
x
14. g(x) 5 22 ? ( 1 __ 3 ) x
−8 −6 −4 −2−2
−4
20 4 6 8
−8
−6
8
6
4
2
y
x
15. g(x) 5 2 1 __ 3 ? 2x
−8 −6 −4 −2−2
−4
20 4 6 8
−8
−6
8
6
4
2
y
x
16. g(x) 5 4 ? ( 1 __ 2 ) x
−8 −6 −4 −2−2
−4
20 4 6 8
−8
−6
8
6
4
2
y
x
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INTRODUCTION TO EXPONENTIAL FUNCTIONS: Skills Practice Answers • 13
Module 3, Topic 1
INTRODUCTION TO EXPONENTIAL FUNCTIONS
17. g(x) 5 4 ? 2(x 2 1)
−8 −6 −4 −2−2
−4
20 4 6 8
−8
−6
8
6
4
2
y
x
18. g(x) 5 21 ? 3x
−8 −6 −4 −2−2
−4
20 4 6 8
−8
−6
8
6
4
2
y
x
19. g(x) 5 32x
−8 −6 −4 −2−2
−4
20 4 6 8
−8
−6
8
6
4
2
y
x
20. g(x) 5 ( 1 __ 2 ) 23x
−8 −6 −4 −2−2
−4
20 4 6 8
−8
−6
8
6
4
2
y
x
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14 • MODULE 3: Investigating Growth and Decay
Module 3, Topic 1
INTRODUCTION TO EXPONENTIAL FUNCTIONS
21. g(x) 5 2 1 __ 2 x
−8 −6 −4 −2−2
−4
20 4 6 8
−8
−6
8
6
4
2
y
x
22. g(x) 5 ( 1 __ 3 ) 24x
−8 −6 −4 −2−2
−4
20 4 6 8
−8
−6
8
6
4
2
y
x
23. g(x) 5 22x 2 1
−8 −6 −4 −2−2
−4
20 4 6 8
−8
−6
8
6
4
2
y
24. g(x) 5 22 ? ( 1 __ 2 ) 22x
−8 −6 −4 −2−2
−4
20 4 6 8
−8
−6
8
6
4
2
y
x
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INTRODUCTION TO EXPONENTIAL FUNCTIONS: Skills Practice Answers • 15
Module 3, Topic 1
INTRODUCTION TO EXPONENTIAL FUNCTIONS
IV. A.
1. 1021
4. x25
2. 1024
5. 527
3. 1023
6. y26
IV. B.
1. 6
4. 27
7. 2
10. 24
2. 4
5. 9
8. 5
11. ]2
3. ]5
6. 22
9. 3
12. 23
IV. C.
1. 15 1
__ 4
4. x 1
__ 3
2. 5 1
__ 3
5. y 1
__ 6
3. 31 1
__ 4
6. z 1
__ 2
IV. D. 1.
3 √ ____
12
4. √ __
a
7. 3 √ ___
52
10. 5 √ ___
x3
2. 5 √ __
7
5. 5 √ __
d
8. 5 √ ___
82
11. 3 √ ___
y 4
3. 4 √ ____
18
6. 6 √ __
c
9. 4 √ ____
183
12. √ ____
m5
IV. E. 1. 6
3
__ 4
4. n 5 __ 2 2. 8 4 __ 5
5. p 7 __ 4 3. 12
2
__ 3
6. m 3
__ 5
IV. F.
1. 3 √ __
2
4. 4 √ __
6
2. 2 √ ____
10
5. 3 √ __
5
3. 10 √ __
2
6. 9 √ ____
10
V. A.
1. x 5 8
3. x 5 6
5. x 5 21
2. x 5 2
4. x 5 2 3 __ 2
6. x 5 27
V. B.
1. 221 ? 2s
2s 2 1
3. 21 ? (22)x
21 ? 22x
22x + 1
5. 43x ? 421
(43)x ? 1 __ 4 64x ? 1 __ 4 1 __ 4 (64)x
The expressions are not equivalent
2. 321 ? 3x
3x 2 1
The expressions are not equivalent.
4. 521 ? 52x
52x 2 1
6. 223x ? 221
(223)x ? 1 __ 2 ( ( 1 __ 2 )
3
) x ? 1 __ 2
( 1 __ 8 ) x ? 1 __ 2
1 __ 2 ( 1 __ 8 ) x
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