Free Printable Exponential Functions Review

1.

Describe this function.

a)

Exponential Growth

b)

Exponential Decay

c)

Linear Positive

2.

a)

Exponential Growth

b)

Exponential Decay

c)

Quadratic

3.

Describe the function.

a)

Exponential Growth

b)

Exponential Deacy

c)

Positive Linear

4.

Describe the function.

a)

Exponential Growth

b)

Exponential Decay

c)

Quadratic

5.

What is the "a" or y-intercept of the equation.

$y\ =\ 5\left(\frac{1}{2}\right)^x$

6.

What is the Growth Factor of the equation.

$y\ =\ 5\left(3\right)^x$

7.

What is the "a" or y-intercept of the function?

a)

2

b)

$\frac{1}{2}$

c)

1

8.

The graph for an exponential function is called a (a)

Choose from the below words

curve

line

parabola

9.

Match the following

a)

1.

Growth

b)

2.

Decay

c)

a

3.

y-intercept

d)

$y\ =\ ab^x$

4.

Exponential Function Equation

e)

b

5.

Growth/Decay Factor

10.

Describe the function. $y\ =\ 5^x$

a)

Growth

b)

Deacy

11.

Describe the function. $y\ =\ 2\left(\frac{1}{2}\right)^x$

a)

Growth

b)

Deacy

12.

Describe the translation.

$y\ =\ 3^x+\ 2$

a)

Up 2

b)

Down 2

13.

Describe the translation.

$y\ =\ 6^x-\ 3$

a)

Up 3

b)

Down 3

14.

Describe the translation.

$y\ =\ 2\left(3\right)^x+\ 7$

(a)

15.

Describe the function.

$y\ =\ 2\left(\frac{1}{2}\right)^x-\ 3$

Exponential function that goes (a) (b)

Choose from the below words

down

3 units

up

2 units

16.

if $y=2^x$ what is y when x = 0, 2, 4?

a)

1, 2 and 8

b)

1, 4 and 16

c)

0, 4 and 8

d)

1, 2 and 8

17.

Which of the following is an exponential function?

a)

y = x²

b)

f(x) = 3x³

c)

$y=\left(-2\right)^x$

d)

f(x) = 3^x

18.

Identify the asymptote of the function $-3\left(3\right)^x+4$

a)

y = -3

b)

y = 1

c)

y = 4

19.

Determine the range for the function

f(x) = 3(2)^x-4+ 5

a)

[5,∞)

b)

(5,∞)

c)

[4,∞)

d)

(4,∞)

20.

What is the range of this function?

a)

(-∞,0)

b)

(0,∞)

c)

(-∞,4)

d)

(4,∞)

21.

The parent function $f\left(x\right)=3^x$ is shown in red and is translated. What is the equation of the green graph?

a)

$g\left(x\right)=3^x+2$

b)

$g\left(x\right)=3^x-2$

c)

$g\left(x\right)=3^{x-2}$

d)

$g\left(x\right)=3^{x+2}$

22.

How has the function $7\left(3\right)^x-5$ been transformed from the parent function $7\left(3\right)^x$ ?

a)

Shifted up 5

b)

Shifted down 5

c)

Reflection over the x-axis

d)

Reflection over the y-axis

23.

What is the domain of the function shown below?

a)

(-2,5)

b)

(0,12)

c)

$\left(0,\infty\right)$

d)

All Real Numbers

24.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

25.

Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)⁶

a)

Growth

b)

Decay

26.

Classify the model as Exponential GROWTH or DECAY.
A=10(1.01)³

a)

Growth

b)

Decay

27.

Is the pictured graph growth, decay, or linear or none?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None

28.

Is this exponential growth or decay?

a)

Growth

b)

Decay

29.

What is the y-intercept of the function?

a)

2

b)

3

c)

1

d)

-2

30.

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

a)

y=6(0.14)^x

b)

y=6(1+14)^x

c)

y=6(1.14)^x

d)

y=6(0.86)^x

31.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

32.

Identify the initial value:

y = 6.87 (4)^x

a)

a = 4

b)

a = 6.87

c)

a = 3

d)

a = 1

33.

The function y = 125(1.13)^xrepresents Mr. Gantz's recent investments where x is measured in years. Which is NOT true?

a)

Mr. Gantz initial invested $125

b)

Mr. Gantz's money grows by 13% per year

c)

After 4 years Mr. Gantz will have about $203.81

d)

Mr. Gantz earns more money in year one than in year 5

34.

Pick the equation that is exponential decay

a)

y=2000(0.88)

b)

y=0.5(1.88)

35.

Is the following function an example of decay or growth?

f(x) = 2(1.25)^x

a)

Exponential Growth

b)

Exponential Decay

36.

Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)⁶

a)

Growth

b)

Decay

37.

Classify the model as Exponential GROWTH or DECAY.
A=10(1.01)³

a)

Growth

b)

Decay

38.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

39.

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

a)

y=6(0.14)^x

b)

y=6(1+14)^x

c)

y=6(1.14)^x

d)

y=6(0.86)^x

40.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

41.

Identify the initial value:

y = 6.87 (4)^x

a)

a = 4

b)

a = 6.87

c)

a = 3

d)

a = 1

42.

What is a, the starting term, for the function: f(x) = 300(1.16)^x?

a)

300

b)

1.16

c)

.16

d)

x

43.

A new savings account is opened with $400 and gains 3% every year. What is the exponential function?

a)

f(x)=400(1+3)^x

b)

f(x)=400(1-0.03)^x

c)

f(x)=400(1+0.03)^x

d)

f(x)=400(0.03)^x

44.

Mike, Randall, and Roz are from which Disney/Pixer animated film?

a)

The Fox and the Hound

b)

Monsters, Inc.

c)

A Bug's Life

d)

The Rescuers

45.

A new savings account is opened with $1500 and gains 1.5% annual interest. What is the exponential function?

a)

f(x)=1500(1+1.5)^x

b)

f(x)=1500(1+0.015)^x

c)

f(x)=1500(1.00375)^x

d)

f(x)=1500(1.5)^x

46.

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation?

a)

y=8(15,000)^x

b)

y=15,000(1.08)^x

c)

y=15,000(0.92)^x

d)

y=15,000(0.08)^x

47.

An adult takes 800 mg of ibuprofen. Each hour, the amount of ibuprofen in the person’s system decreases by about 29%. How much ibuprofen is left after 6 hours? (hint: create equation first)

a)

101

b)

102

c)

103

d)

104

48.

The amount of ibuprofen (medicine for headaches) breaks down by 30% each hour. If a person took a 200 milligram ibuprofen, how much will be left after 3 hours?

a)

5.4 mg

b)

68.6 mg

c)

.0054 mg

d)

2,400,000 mg

49.

The expression 12(1.015)^t models the population of elephants in a wildlife refuge after t years since 1975.
What does the value 1.015 represent?

a)

The number of elephants was 1,015 in 1975.

b)

The number of elephants increases by 1.5% each year.

c)

The number of elephants increases by 101.5% each year.

d)

The number of elephants is multiplied by 1.015 each year.

50.

The expression 12(1.015)^t models the population of elephants in a wildlife refuge after t years since 1975.
What does the value 12 represent?

a)

The predicted increase in number of elephants in the refuge each year.

b)

The predicted decrease in number of elephants in the refuge each year.

c)

The number of years it will take for the elephant population to stop increasing.

d)

The initial amount of elephants in the park.

51.

The expression 12(1.015)^t models the population of elephants in a wildlife refuge after t years since 1975.
Is the population of elephants increasing or decreasing?

a)

Increasing

b)

Decreasing

52.

The amount of downloads for an album on iTunes, g(d), where d is the number of days since the album was first uploaded can be represented as
g(d) = 5^1.5d
How many downloads will the album have after 3 days?

a)

125

b)

11

c)

1398

d)

140

53.

What does r represent in the explicit formula for a geometric sequence?

a)

Radical

b)

Common Ratio

c)

Common Difference

54.

Find the common ratio for the geometric sequence:

10,\ 20,\ 40,\ 80

a)

10

b)

1/2

c)

2

d)

4

55.

Find the common ratio of the following geometric sequence

-250,\ -50,\ -10,\ 2

a)

r = 5

b)

r = -5

c)

r = 1/5

d)

r = -1/5

56.

Is the following sequence geometric?

a)

Yes

b)

No

57.

Is the following sequence geometric?

2,\ 4,\ 12,\ 48

a)

Yes

b)

No

58.

$3,\ 24,\ 192,\ 1536$

Write the explicit formula for the following geometric sequence

a)

$a_n=8\cdot3^{n-1}$

b)

$a_n=3\cdot8^{n-1}$

c)

$a_n=3+8\left(n-1\right)$

59.

Which formula is the recursive equation for a geometric sequence?

a)

a_1=

a_n=r\cdot a_{n-1}

b)

$a_n=a_1+d\left(n-1\right)$

c)

$a_n=a_1\cdot r^{n-1}$

d)

$a_1=$
$a_n=d+a_{n-1}$

60.

Write the recursive formula for the following sequence

16,\ 8,\ 4,\ 2

a)

a_1=16

a_n=\frac{1}{2}\cdot a_{n-1}

b)

$a_1=16$

a_n=2\cdot a_{n-1}

c)

$a_1=16$
$a_n=a_{n-1}-8$

d)

$a_1=16$

a_n=a_{n-1}+0.5

61.

Given the recursive formula, write the explicit formula for the geometric sequence.

a_1=6

a_n=5\cdot a_{n-1}

a)

$a_n=5\cdot6^{n-1}$

b)

$a_n=6\cdot5^{n-1}$

c)

$a_n=6+5\left(n-1\right)$

d)

$a_n=5+6\left(n-1\right)$

62.

What is the common ratio for the sequence:
28, 14, 7, 3.5...

a)

2

b)

1/2

c)

-14

d)

-7

63.

Find the common ratio: 4, -16, 64, -256, ...

a)

r = -4

b)

r = 2

c)

r = -2

d)

r = 4

64.

Find the common ratio for the following geometric sequence:

7, -7, 7, -7, ...

a)

1

b)

-1

c)

7

d)

-7

65.

Find the next three terms: -4, -12, -36, -108, ...

a)

36, -108, 324

b)

-324, -972, -2916

c)

324, -972, 2916

d)

-108, 324, -972

66.

Write an explicit rule for the general term of the sequence 5, 15, 45, . . . ?

a)

a_n = a_n-1 x 3

b)

a_n = 5(3)^n-1

c)

a_n = 3(5)^n-1

d)

a_n = 5 + (n-1)3

67.

Write the explicit formula for the following geometric sequence:

10, 20, 40, 80, ...

a)

a_n = 10(2)^n-1

b)

a_n = 2(10)^n-1

c)

a_n = 10(2)ⁿ

d)

a_n = 2(10)ⁿ

68.

Write the explicit rule for the following geometric sequence:

2, -12, 72, ...

a)

a_n = 72(-6)^n-1

b)

a_n = 2(-6)^n-1

c)

a_n = 2(6)^n-1

d)

a_n = 72(-6)^n-1

69.

Write the explicit formula for the following geometric sequence:

3, -12, 48, -192, ...

a)

a_n = 4(3)^n-1

b)

a_n = 3(4)^n-1

c)

a_n = -4(3)^n-1

d)

a_n = 3(-4)^n-1

70.

Find the first four terms of the sequence given the rule:
a_n = 4(5)^n-1

a)

20, 100, 500, 2500

b)

5, 20, 80, 320

c)

4, 20, 100, 500

d)

4, 9, 14, 19

71.

Which sequence is represented by the equation 2(7)^n-1 ?

a)

7, 14, 28, 56...

b)

2, 14, 98, 686...

c)

2, 9, 16, 23...

d)

7,9,11,13...

72.

Find the 11^th term for: 64, -32, 16, -8, …

a)

-.0625

b)

.0625

c)

-.03125

d)

.03125

73.

Find the 9th term in the following geometric sequence:

4, 8, 16, 32, ...

a)

384

b)

512

c)

768

d)

1,024

74.

Find a₁₁ in the following geometric sequence:

-3, 6, -12, 24

a)

-4,096

b)

-¹/₂₅₆

c)

-3,072

d)

-236,196

75.

Find a₁₂ in the sequence -1, -3, -9, -27, ...

a)

-177,147

b)

-19,683

c)

-59,049

d)

118,098

76.

Find a₁₂ for the geometric sequence defined by the following formula:

a_n = 6(2)^n-1

a)

4096

b)

24,576

c)

2048

d)

12,288

77.

Is this sequence Arithmetic, Geometric, or Neither?

2, 9, 7, 14, 12, 19, ...

a)

Arithmetic

b)

Geometric

c)

Neither

78.

Which sequence is an arithmetic sequence?

a)

3, 6, 2, 7, ...

b)

3, 6, 12, 24, ...

c)

3, 6, 10, 15, ...

d)

3, 7, 11, 15, ...

79.

Which sequence is a geometric sequence with a common ratio of 2?

a)

5, 3, 1, -1, ...

b)

5, 7, 9, 11, ...

c)

5, 10, 20, 40, ...

d)

5, 15, 45, 135, ...

80.

What is the common difference of the arithmetic sequence below?
-6, -1, 4, 9...

a)

5

b)

-5

c)

-6

d)

1/5

81.

The next term of the series 11,8,5,2 is...

a)

-1

b)

-2

c)

1

d)

2

82.

What is the common ratio of the geometric sequence below?
5, 25, 125, 625...

a)

25

b)

20

c)

5

d)

4

83.

What is the common ratio in this sequence?

96, 48, 24, 12, ...

a)

1/2

b)

2

c)

12

d)

24

84.

The first term in an arithmetic sequence is -8 and the common difference is 14. What is the 28th term given the equation a_n= a₁ + d (n - 1)

a)

378

b)

1024

c)

-324

d)

370

85.

The first term in a geometric sequence is 160 and the common ratio is 1/2. What is the 7th term given the equation a_n= a₁(r)^n-1

a)

5

b)

2.5

c)

10

d)

1.25

86.

What does r represent?

a)

Radical

b)

Common difference

c)

Common ratio

87.

What does a₁ represent?

a)

Any term

b)

First term

c)

Last term

88.

What does n represent?

a)

Number

b)

Nothing

c)

Term you are trying to find

89.

Is the sequence -432, 72, -12, 2,...geometric?

a)

yes

b)

no

90.

Determine whether the sequence is arithmetic, geometric, or neither.

a)

arithmetic

b)

geometric

c)

neither

91.

Determine whether the sequence is arithmetic, geometric, or neither.

a)

arithmetic

b)

geometric

c)

neither

92.

Find the common ratio for the geometric sequence.

a)

10

b)

1/2

c)

2

d)

4

93.

Find the common ratio for the geometric sequence.

a)

1

b)

-1

c)

7

d)

-7

94.

This image shows how a certain bacteria grows in a petri dish. What is the common ratio of this sequence?

a)

4

b)

3

c)

2

d)

6

95.

Write the explicit formula for the geometric sequence.

a)

a_n = 4(3)^n-1

b)

a_n = 3(4)^n-1

c)

a_n = -4(3)^n-1

d)

a_n = 3(-4)^n-1

96.

Given the sequence:

125, 25, 5, ....

Write the rule a_n using the geometric sequence formula:

a)

a_n = (125)(1/5)^(n-1)

b)

a_n = 625(1/5)^(n-1)

c)

a_n = 625(5)^(n-1)

d)

a_n = 125 + 5n

97.

What are the next 3 terms in the following geometric sequence:

512, 256, 128, ___, ___, ___, ...

a)

1024, 2048, 4096

b)

32, 8, 2

c)

64, 32, 16

d)

92, 66, 38

98.

Find the first four terms of the sequence given the rule:
a_n = 4(5)^n-1

a)

20, 100, 500, 2500

b)

5, 20, 80, 320

c)

4, 20, 100, 500

d)

4, 9, 14, 19

99.

What is the 14th term of the geometric sequence?

a)

14,348,907

b)

4,782,969

c)

1,594,323

d)

45

100.

Find a₁₂ in the sequence -1, -3, -9, -27, ...

a)

-177,147

b)

-19,683

c)

-59,049

d)

118,098

101.

What is the 9^th term in a geometric sequence with a common ratio of 2 and a first term of 3?

a)

384

b)

768

c)

1,536

d)

27

102.

Daisy received $2 on her first birthday. Each year, the amount of money she received tripled. How much money will she receive on her 5^th birthday?

a)

$10

b)

$300

c)

$162

d)

$416

103.

You have $10 in you bank account. It doubles every month. How much money will you have after 5 months?

a)

$50

b)

$35

c)

$320

d)

$250

104.

A geometric sequence has a common ration(r) of 3 and the 8th term (a₈) is 13,122. What is the first term of the sequence (a₁)?

a)

3

b)

6

c)

18

d)

2

105.

A geometric sequence has a common ration(r) of 2 and the 13th term (a₁₃) is 36,864. What is the first term of the sequence (a₁)?

a)

3

b)

9

c)

18

d)

6

Exponential Functions Review

Total questions: 105

Worksheet time: 5hrs 15mins

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