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Module 3, Topic 1

INTRODUCTION TO EXPONENTIAL FUNCTIONS

Answer Key

I. A.

1.

f(n)

5

_5_ 2

?

2n

y

2700 2400 2100 1800 1500 1200

900 600 300

0 123456789 x

2. f(n) 5 21 ? 3n

y

? 10,000 0 1 2 3 4 5 6 7 8 9 x ? 20,000 ? 30,000 ? 40,000 ? 50,000 ? 60,000 ? 70,000 ? 80,000

3. f(n) 5 8 ? 2.5n

y

90,000 80,000 70,000 60,000 50,000 40,000 30,000 20,000 10,000

0 123456789 x

4. f(n) 5 1000 ? 0.9n

y

900 800 700 600 500 400 300 200 100

0 123456789 x

? Carnegie Learning, Inc.

INTRODUCTION TO EXPONENTIAL FUNCTIONS: Skills Practice Answers ? 1

Module 3, Topic 1

INTRODUCTION TO EXPONENTIAL FUNCTIONS

5. f(n) 5 20.25 ? 2n

y

? 30 0 1 2 3 4 5 6 7 8 9 x ? 60 ? 90 ? 120 ? 150 ? 180 ? 210 ? 240

6. f(n) 5 1000 ? 1.25n

y

9000 8000 7000 6000 5000 4000 3000 2000 1000

0 123456789 x

? Carnegie Learning, Inc.

2 ? MODULE 3: Investigating Growth and Decay

Module 3, Topic 1

INTRODUCTION TO EXPONENTIAL FUNCTIONS

II. A.

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)

y

4 3 2 1

-4 -3 -2 -1

01 2 3 4

x

-1

-2

-3

-4

y

16 12

8 4

-16 -12 -8 -4 0 4 8 12 16 x -4 -8

-12 -16

? Carnegie Learning, Inc.

INTRODUCTION TO EXPONENTIAL FUNCTIONS: Skills Practice Answers ? 3

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)

y

8 6 4 2

-8 -6 -4 -2

02 4 6 8

x

-2

-4

-6

-8

y

16 12

8 4

-16 -12 -8 -4 0 4 8 12 16 x -4 -8

-12 -16

? Carnegie Learning, Inc.

4 ? MODULE 3: Investigating Growth and Decay

5.

x

f(x)

22

2_12_

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_12_

constant

ratio:

_1_ 2

y-intercept: (0, 22)

Module 3, Topic 1

INTRODUCTION TO EXPONENTIAL FUNCTIONS

y

8 6 4 2

-8 -6 -4 -2

02 4 6 8

x

-2

-4

-6

-8

y

8 6 4 2

-8 -6 -4 -2

02 4 6 8

x

-2

-4

-6

-8

? Carnegie Learning, Inc.

INTRODUCTION TO EXPONENTIAL FUNCTIONS: Skills Practice Answers ? 5

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