Free Printable Alg 1 Exponents Practice

1.

In March, 2020, before the Covid-19 lockdown, 1,200,000 Texans had applied for unemployment. During the COVID-19 lockdown, the number of people applying for unemployment increased by 4% each month. What exponential function can be used to find the number of people applying for unemployment after x months of COVID-19 lockdown? (a)

Choose from the below words

$y=1,200,000\left(1.04\right)^x$

$y=\ 1,200,000\left(0.04\right)^x$

$y=1,200,000\left(1.4\right)^x$

$y=1,200,000\left(0.06\right)^x$

2.

Which of the following exponential functions represents an initial value of 1450 and a decay of 18% for x years?

a)

$y=1450\left(0.18\right)^x$

b)

$y=1450\left(1.18\right)^x$

c)

$y\ =\ 1450\ -\left(0.18\right)^x$

d)

$y=1450\left(0.82\right)^x$

3.

Which of the following exponential functions represents an initial value of 1780 and a growth of 18% for x years?

(a)

Choose from the below words

$y=1780\left(1.18\right)^x$

$y=1780\left(0.18\right)^x$

$y=\ 1780\ -\ \left(0.18\right)^x$

$y=1780\left(.82\right)$

4.

Chloe was studying earthquake waves in Japan. The function of $f\left(x\right)=354\left(1.15\right)^x$ gives the number of waves at the end of x days. What is the growth rate for this function?

a)

The initial number of waves is 15.

b)

The initial number of waves decreases at a rate of 85% each day.

c)

The initial number of waves increases at a rate of 15% each day.

d)

The number of waves at the end of one day is 354.

5.

The current population of India (2021) is 1.393 billion people, at an annual rate of increase of 97%. Which exponential function models the population, in billions of people, of India after x number of years?

(a)

Choose from the below words

$P\left(x\right)=1.393\left(1.97\right)^x$

$P\left(x\right)=1.393\left(0.3^x\right)$

$P\left(x\right)=1.393\left(1.3\right)^x$

$P\left(x\right)=1.393\left(0.97\right)^x$

6.

A flea medicine breaks down at a rate of 20% per hour. This is the rate of decay of the medicine. The initial dose is 60 milligrams. Which of the following represent the equation the models the amount of flea medicine left in an animal?

a)

$y=60\left(.2\right)^x$

b)

$y=20\left(60\right)^x$

c)

$y=60\left(.8\right)^x$

d)

$y=60\left(1.2\right)^x$

7.

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

a)

Growth

b)

Decay

8.

This is an example of:

(a)

Choose from the below words

Exponential Growth

Linear Growth

Linear Decay

Exponential Decay

9.

This is an example of:

a)

Linear Growth

b)

Linear Decay

c)

Exponential Growth

d)

Exponential Decay

10.

Select all the equations that represent exponential decay.

a)

$y=\frac{1}{2}\left(4\right)^x$

b)

$y=4\left(\frac{1}{2}\right)^x$

c)

$y=80\left(1.4\right)^x$

d)

$y=60\left(0.7\right)^x$

e)

$y=3\left(0.6\right)^x$

11.

Which number is the BASE?
2³= 8

a)

2

b)

3

c)

8

d)

not here

12.

What is the value of 100⁰?

a)

1

b)

0

c)

100

13.

What is the exponent form for
6?

a)

6⁰

b)

6¹

c)

6×1

d)

0

14.

Write each product using an exponent.
7 x 7 x 7 x 7 x 7 x 7 x 7 x 7

a)

7⁷

b)

7⁸

c)

8⁷

d)

7⁹

15.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same

d)

Zero is greater

16.

Simplify the expression: 3x²⋅x²=

a)

3x

b)

3x²⁺²

c)

3x⁴

17.

Simplify the expression:
c⁴⋅c³=

a)

^c12

b)

c⁴⁺³

c)

c⁷

18.

According to exponent rules, when we raise a power to another exponent we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

19.

(2⁸)²

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

20.

x⁶ / x²

a)

x⁴

b)

x¹²

c)

x³

d)

x⁸

21.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

22.

Which is GREATER?
2⁷ or 7²

a)

2⁷

b)

7²

c)

Neither, they are equal

23.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same

d)

Zero is greater

24.

Which expression is equivalent to 3⁴?

a)

3+3+3+3

b)

4+4+4

c)

4x4x4

d)

3x3x3x3

25.

Which expression is equivalent to 10⁶?

a)

1,000,000

b)

60

c)

3,294,360

d)

600

26.

Which expression is not equivalent to 81?

a)

3⁴

b)

9²

c)

81¹

d)

27³

27.

(c⁵)(c³)(c³)

a)

c⁴⁵

b)

3c¹¹

c)

c¹¹

d)

3c⁴⁵

28.

(2⁸)²

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

29.

(g⁵)⁸

a)

g¹³

b)

5g⁸

c)

g⁴⁰

d)

8g⁵

30.

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

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None

31.

Is y = 4(.20)^x growth or decay?

a)

Growth

b)

Decay

32.

What is the initial amount for the function: f(x) = 300(1.16)^x?

a)

300

b)

1.16

c)

.16

d)

x

33.

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

34.

Classify the model as Exponential GROWTH or DECAY.

$A=10(1.01)^3$

a)

Growth $y=a\left(1+r\right)^t$

b)

Decay $y=a\left(1-r\right)^t$

35.

Classify the model as Exponential GROWTH or DECAY.

$A=1200(.85)^6$

a)

Growth $y=a\left(1+r\right)^t$

b)

Decay $y=a\left(1-r\right)^t$

36.

Pick the equation that is exponential decay

a)

y=2000(0.88)

b)

y=0.5(1.88)

37.

An antibiotic is introduced into a colony of 12,000 bacteria during a laboratory experiment. The colony is decreasing by 14.9% per minute. Which function can be used to model the number of bacteria in the colony after x minutes?

a)

f(x) = 12000(1 + 14.9)^x

b)

f(x) = 12000(1 - 14.9)^x

c)

f(x) = 12000(1 + 0.149)^x

d)

f(x) = 12000(1 - 0.149)^x

38.

Twenty years ago, Mr. Davis purchased his home for $160,000. Since then, the value of the home has increased about 5% per year. How much is the home worth today?

a)

$176,783.29

b)

$424,527.63

c)

$57,357.75

d)

$532,041,076.80

39.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

a)

y=5000(0.7)^x

b)

y=30(5000)^x

c)

y=5000(1.3)^x

d)

y=5000x^x

40.

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

41.

Moody's Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?

a)

$23,219.72

b)

$136.72

c)

$51,710.94

d)

$16,710.94

42.

Which color functions is exponential?

a)

Blue

b)

Green

c)

Red

d)

Yellow

43.

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

44.

What type of function is y = 7(5/4)^x?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None of the above

45.

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

a)

Growth

b)

Decay

46.

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

a)

300

b)

1.16

c)

.16

d)

x

47.

A 78 gram sample of Uranium loses half of its mass each year. What is the exponential equation?

a)

y=78(0.5)^x

b)

y=78(1.5)^x

c)

y=78(2)^x

48.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

a)

y=5000(0.7)^x

b)

y=30(5000)^x

c)

y=5000(1.3)^x

d)

y=5000x^x

49.

Is this exponential growth or decay?

a)

Growth

b)

Decay

c)

Linear

50.

What does the a in y=a(1+r)^x represent?

a)

Time

b)

Rate

c)

Slope

d)

Initial Amount

51.

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

52.

What type of function is f(x)=2(1/7)^x ?

a)

Exponential Growth

b)

Linear

c)

Exponential Decay

d)

None of the Abovee

53.

What is the decay rate in the following model?

A=1200(.85)⁶

a)

1200

b)

.15

c)

.85

d)

6

54.

What is the decay factor in the following model?
A=1200(.85)⁶

a)

1200

b)

-.15

c)

.85

d)

A

55.

Is this exponential growth or decay?

a)

Growth

b)

Decay

56.

What is r, the growth rate, for the function: f(x) = 300(1.16)^x?

a)

300

b)

1.16

c)

.16

d)

x

57.

Is y = 5(1.04)^x growth or decay?

a)

Growth

b)

Decay

58.

Is y = 4(.20)^x growth or decay?

a)

Growth

b)

Decay

59.

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months?

a)

9766

b)

9006

c)

9765

d)

5433

60.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

a)

y=5000(0.7)^x

b)

y=30(5000)^x

c)

y=5000(1.3)^x

d)

y=5000x^x

61.

Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?

a)

$23,219.72

b)

$136.72

c)

$51,710.94

d)

$16,710.94

62.

A line that the graph continually approaches but never touches is a(n) _____________________

a)

parabola

b)

asymptote

c)

rational function

d)

None of these

63.

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

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None

64.

Is the graph linear, exponential or neither?

a)

Linear

b)

Exponential

c)

Neither

65.

What is the y-intercept?

a)

(0,0)

b)

(0,1)

c)

(-3,0)

d)

(0,-3)

66.

What is the asymptote of y = 2^x ?

a)

y = 0

b)

x = 0

67.

What is the asymptote of y = 2^x - 3

a)

y = 0

b)

y = -3

c)

x = 0

d)

x = -3

68.

What is the asymptote of y = 2^x-3 ?

a)

y = 0

b)

y = -3

c)

x = 0

d)

x = -3

69.

The asymptote is

a)

y = 3

b)

x = 3

c)

y = 2

d)

x = 2

70.

As x → ∞ , f(x) →

a)

-4

b)

-3

c)

∞

d)

-∞

71.

Which equation matches the graph?

a)

y = 4^x + 3

b)

y = 4^x - 3

c)

y = 4^{(x + 3)}

d)

y = 4^{(x - 3)}

72.

What is the domain of the function?

a)

x > -4

b)

y > -5

c)

y < -4

d)

all real numbers

73.

What is the asymptote for the equation $y=2^{x+5}-7$ ?

a)

y = -7

b)

y = 7

c)

y = 5

d)

x = 2

74.

What is the range of this graph?

a)

y = 6

b)

(0, -4)

c)

y > -6

d)

y < -6

75.

Domain?

a)

ℝ

b)

y > 0

c)

y < 0

d)

y ≥ 0

76.

Compare f(x) = 3^x- 4 with the basic function g(x) = 3^x

a)

4 units up

b)

4 units to the left

c)

4 units to the right

d)

4 units down

77.

Is the equation linear, exponential, or quadratic?
y = 2^x

a)

Linear

b)

Exponential

c)

Quadratic

d)

None of the above

78.

The point (1,0) is:

a)

a zero

b)

the y-intercept

c)

the domain

d)

the range

79.

On the graph y = 4^x + 2.

What is the y-intercept?

a)

(0, 1)

b)

(0, 4)

c)

(0, 2)

d)

(0, 3)

80.

What is the transformation?

a)

Left 5

b)

Right 5

c)

Up 5

d)

Down 5

81.

Which exponential equation could represent the graph shown?

a)

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

b)

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

c)

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

d)

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

82.

Which graph shows a reflection of

f\left(x\right)=3^x

over the x-axis?

a)

b)

83.

Warm-Up #1: Match the following graphs as linear or absolute value

a)

1.

Absolute Value

b)

2.

Linear

c)

3.

Neither

84.

Warm Up #2: Match the following

a)

1.

Linear

b)

2.

Absolute Value

c)

3.

Neither

85.

Which of the following is an exponential function?

a)

$f\left(x\right)=x^2$

b)

$f\left(x\right)=3x^3$

c)

$y=x^3$

d)

$f\left(x\right)=3^x$

86.

Does the table represent a linear or exponential function?

a)

Linear

b)

Exponential

87.

Does the table represent a linear of exponential function?

a)

Linear

b)

Exponential

88.

What is the initial value in

$y=25\left(4\right)^x$

a)

25

b)

4

c)

x

89.

What is the growth or decay factor for the equation

$f\left(x\right)\ =\ 25\left(4\right)^x$

a)

25

b)

4

90.

Select all the equations that represent exponential decay.

a)

$y=\frac{1}{2}\left(4\right)^x$

b)

$y=4\left(\frac{1}{2}\right)^x$

c)

$y=80\left(1.4\right)^x$

d)

$y=60\left(0.7\right)^x$

e)

$y=3\left(0.6\right)^x$

91.

Select the functions that are exponential growth.

a)

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

b)

$f\left(x\right)=3\left(1.09\right)^x$

c)

$f\left(x\right)=4\left(\frac{1}{3}\right)^x$

d)

$y=0.5\left(\frac{3}{2}\right)^x$

92.

Classify the equation $y\ =\ 120\left(\frac{1}{7}\right)^x$

a)

Growth

b)

Decay

c)

Linear

93.

Identify the growth/decay value $y\ =120\left(\frac{1}{7}\right)^x$

a)

120

b)

$\frac{1}{7}$

c)

x

94.

Which graph represents exponential growth?

a)

b)

c)

d)

95.

Which graph represents exponential decay?

a)

b)

c)

d)

96.

What is the range of this graph?

a)

y = 6

b)

(0, -4)

c)

y > -6

d)

y < -6

97.

Domain?

a)

ℝ

b)

y > 0

c)

y < 0

d)

y ≥ 0

98.

Range?

a)

y > -8

b)

y > 0

c)

y < -8

d)

y < 0

99.

Range?

a)

y < 2

b)

y < -2

c)

y > 2

d)

y > -2

100.

Find the domain.

a)

x < 1

b)

ℝ

c)

x > 0

d)

x < 0

101.

Which equation best describes the graph?

a)

y = 2^x + 4

b)

y = 2^x - 3

c)

y = 2^x - 4

d)

y = 2^x + 3

102.

Compare f(x) = 3^x- 4 with the basic function g(x) = 3^x

a)

4 units up

b)

4 units to the left

c)

4 units to the right

d)

4 units down

103.

What kind of transformation is represented?

a)

up 1 unit

b)

left 1 unit

c)

right 1 unit

d)

down 1 unit

104.

Change 6.75% to a decimal.

a)

67.5

b)

.675

c)

675

d)

.0675

105.

What does the n stand for in this formula?

a)

Initial amount

b)

Final amount

c)

Rate

d)

Time

e)

The number of times compounded per year

106.

Kennedy won $3,000 from a radio contest. If she puts this money in a bank account that earns 2.9% interest compounded quarterly, how much total will she earn in 10 years?

a)

$4915.59

b)

$3933.28

c)

$2979.81

d)

$4005.09

107.

Caiden earned $475 from mowing lawns last summer. He deposited this money in an account that pays an interest rate of 3.8% compounded annually. What will be his balance after 15 year?

a)

$827.52

b)

$831.10

c)

$839.45

d)

$846.80

108.

The Arnold's took out a loan for $195,000 to purchase a home. At a 4.3% interest rate compounded annually, how much total will they have paid after 30 years?

a)

$412,749.79

b)

$529.305.61

c)

$689,546.99

d)

$640,891.53

109.

Olivia would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years.

a)

$15,415.94

b)

$15,683.28

c)

$15,927.56

d)

$16,109.05

110.

Caiden earned $475 from mowing lawns last summer. He deposited this money in an account that pays an interest rate of 3.8% compounded annually. What will be his balance after 15 year?

a)

$827.52

b)

$831.10

c)

$839.45

d)

$846.80

111.

You invest $1600 at an annual interest rate of 4.6% compounded continuously. How much will you have in the account after 4 years.

a)

$800.26

b)

$6,701.28

c)

$10,138.07

d)

$1,923.23

112.

Determine the balance in the account if you deposited $4,000 at an interest rate of 3.4% compounded monthly for three years.

a)

$4422.03

b)

$4427.62

c)

$4428.90

d)

$4429.51

113.

Determine the balance in the account if you deposited $4,000 at an interest rate of 3.4% compounded quarterly for three years.

a)

$4422.03

b)

$4427.62

c)

$4428.90

d)

$4429.51

114.

Simply the expression. $e^{-4}\cdot e^6$

a)

$e^{-2}$

b)

$\frac{1}{e^2}$

c)

$e^2$

d)

$e^{24}$

e)

$e^{-24}$

115.

Simplify the expression. $\frac{11e^9}{22e^{10}}$

a)

$\frac{2}{e}$

b)

$\frac{1}{2e}$

c)

$\frac{e^{-1}}{2}$

d)

$2e$

116.

Simplify: $\left(4e^{-2x}\right)^3$

a)

$\frac{4}{e^{6x}}$

b)

$\frac{1}{64e^{6x}}$

c)

$64e^{6x}$

d)

$\frac{64}{e^{6x}}$

117.

Find the mistake in the problem.

a)

They should have subtracted the exponents.

b)

They should have added the exponents.

c)

They should have multiplied the exponents.

d)

They should have divided the exponents.

118.

Correct the error & choose the simplified answer.

a)

$e^{-10x}$

b)

$e^{7x}$

c)

$e^{3x}$

d)

$e^{-\frac{5}{2}x}$

119.

Caiden earned $475 from mowing lawns last summer. He deposited this money in an account that pays an interest rate of 3.8% compounded monthly. What will be his balance after 15 years?

a)

$827.52

b)

$839.17

c)

$839.45

d)

$846.80

120.

Determine the balance in the account if you deposited $4,000 at an interest rate of 3.4% compounded quarterly for three years.

a)

$4422.03

b)

$4427.62

c)

$4428.90

d)

$4429.51

121.

The Arnold's took out a loan for $195,000 to purchase a home. At a 4.3% interest rate compounded annually, how much total will they have paid after 30 years?

a)

$412,749.79

b)

$529.305.61

c)

$689,546.99

d)

$640,891.53

122.

You invest $1600 at an annual interest rate of 4.6% compounded continuously. How much will you have in the account after 4 years.

a)

$800.26

b)

$6,701.28

c)

$10,138.07

d)

$1,923.23

123.

What does the P stand for in this formula?

a)

Initial amount

b)

Final amount

c)

Rate

d)

Time

e)

The number of times compounded per year

124.

Kennedy won $3,000 from a radio contest. If she puts this money in a bank account that earns 2.9% interest compounded quarterly, how much total will she earn in 10 years?

a)

$4915.59

b)

$3933.28

c)

$2979.81

d)

$4005.09

125.

Change 6.75% to a decimal.

a)

67.5

b)

.675

c)

675

d)

.0675

126.

What does the n stand for in this formula?

a)

Initial amount

b)

Final amount

c)

Rate

d)

Time

e)

The number of times compounded per year

127.

If you deposit $8,000 into an account paying 7% annual interest compounded quarterly, how long until there is $12,400 in the account?

a)

.83 yrs

b)

6.5 yrs

c)

40.5 yrs

d)

-6.5 yrs

128.

Hugo opened a savings account and deposited $800 as principal. The account earns 4% interest, compounded continuously. What is the balance after 5 years?

a)

$832.00

b)

$977.12

c)

$973.32

d)

$960.00

129.

Travis earned $180.72 doing odd jobs last summer and put it in a saving account that earns 15% interest compounded continuously. If he doesn't touch his money for 8 years, how much will he have?

a)

$400

b)

$500

c)

$553

d)

$600

Alg 1 Exponents Practice

Total questions: 129

Worksheet time: 4hrs 15mins

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