Free Printable Unit 2- Exponents Review

1.

There were 417 cell phones sold at an electronics store in January. Since then, cell phone sales at this store have increased at a rate of 3.75% per month. At this rate of growth, which function can be used to determine the monthly cell phone sales x months after January?

a)

f(x) = 417(3.75)^x

b)

f(x) = 417(0.0375)^x

c)

f(x) = 417(1.0375)^x

d)

f(x) = 417(1.375)^x

2.

Some banks charge a fee for a savings account that is left inactive for an extended period of time. The equation y = 5000(0.98)^x represents the amount remaining, y, of one account that was left inactive for a period of x years. What does the number 5000 represent in this situation?

a)

A fee charged for an inactive account

b)

The percent of money in the account after x years

c)

The amount of money in the account initially

d)

The amount of money in the account after x years

3.

A child asks her dad for an allowance that starts with a penny and then doubles every day for a month. Which function can be used to model the amount of money, A, the child will receive each day, x?

a)

A(x) = 2(0.01)^x

b)

A(x) = 0.01(2)^x

c)

A(x) = 0.01(1 - 2)^x

d)

A(x) = 2(1.01)^x

4.

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

5.

The population of Winnemucca, Nevada, can be modeled by P=6191(1.04)^twhere t is the number of years since 1990. What was the population in 1990?

a)

0 people

b)

1.04 people

c)

6191 people

6.

The population of Winnemucca, Nevada, can be modeled by P=6191(1.04)^t where t is the number of years since 1990. What percent did the population increase each year?

a)

4%

b)

104%

c)

96%

d)

1.04%

7.

An adult takes 400 mg of ibuprofen. Each hour, the amount of ibuprofen in the person’s system decreases by about 29%.

What is the multiplier (the b-value) for this problem?

a)

1.29

b)

.71

c)

.29

d)

1.71

8.

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(0.35)^x

c)

y = 15(1.35)^x

d)

y = 35(1.15)^x

9.

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)

9765

b)

9006

c)

5433

d)

9766

10.

Which of the following functions shows an initial amount of $15,000 and a decrease of 12% each year?

a)

y = 15000(0.88)^x

b)

y = 15000(0.12)^x

c)

y = 15000(1.12)^x

d)

y = 15000(1.88)^x

11.

Rhonda deposited $3000 in an account in the Merrick National Bank, earning 4.2% interest, compounded annually. She made no deposits or withdrawals. Write an equation that can be used to find B, her account balance after t years.

a)

B = 3000(1 – 4.2)^t

b)

B = 3000(1 + 4.2)^t

c)

B = 3000(1 – 0.042)^t

d)

B = 3000(1 + 0.042)^t

12.

Marilyn collects old dolls. She purchases a doll for $450. Research shows this doll's value will increase by 2.5% each year. Write an equation that determines the value, V, of the doll t years after purchase.

a)

V = 450(1 + 0.025)^t

b)

V = 450(1 – 0.025)^t

c)

V = 450(1 + 2.5)^t

d)

V = 450(1 – 2.5)^t

13.

A car was purchased for $25,000. Research shows that the car has an average yearly depreciation rate of 18.5%. Create a function that will determine the value, V(t), of the car t years after purchase.

a)

V(t) = 25000(1 – 0.185)^t

b)

V(t) = 25000(1 + 0.185)^t

c)

V(t) = 25000(1 – 18.5)^t

d)

V(t) = 25000(1 + 18.5)^t

14.

The bear population in a given area is currently 1580. They anticipate the bear population to decrease by 2% each year. Which function represents the population of bears, B, after t years.

a)

B = 1580(0.02)^t

b)

B = 1580(1 – 0.02)^t

c)

B = 1580(1 + 0.02)^t

d)

B = 1580(1 – 0.2)^t

15.

The population of a town is currently 6342 and is increasing by a rate of 1.3% each year. Which function represents the population of people, P, after t years.

a)

P = 6342(1 + 1.3)^t

b)

P = 6342(1 – 1.3)^t

c)

P = 6342(1 + .013)^t

d)

P = 6342(1 – .013)^t

16.

Change .67 to a percent

a)

67%

b)

.0067%

c)

.67%

d)

670%

17.

Change .384 to a percent

a)

384%

b)

38.4%

c)

.00348%

d)

3.84%

18.

1/2 is what decimal ?

a)

.25

b)

.50

c)

.35

d)

.40

19.

Change 4% to a decimal

a)

.4

b)

.40

c)

.04

d)

400

20.

Write 57% as a decimal.

a)

0.57

b)

05.7

c)

570

21.

Solve: 7^-x = 49

a)

x = 1

b)

x = -1

c)

x = 2

d)

x = -2

22.

Solve: 2^x = 4^x+1

a)

x = -2

b)

x = 2

c)

x = -3

d)

x = 3

23.

Sovle for x:
5^{-3x - 1} = 25

a)

x = -1

b)

x = -4

c)

x = -3

d)

x = 1

24.

Solve 3³ = 3^{4x + 2}

a)

x = ¼

b)

x = -¼

c)

x = ½

d)

x = -½

25.

Solve for p:
4^p+2 = 64

a)

p = -16/9

b)

p = 1

c)

p = 8

d)

p = 7/6

26.

To solve 36 = 6^x, re-write 36 as what base and exponent?

a)

3⁶

b)

6³

c)

6²

d)

3¹²

27.

To solve 8 = 2^5x+7, you would need to re-write 8 as what base?

a)

8

b)

4

c)

2

d)

Cannot be determined

28.

Change 6.75% to a decimal.

a)

67.5

b)

.675

c)

675

d)

.0675

29.

Is the graph linear, exponential or neither?

a)

Linear

b)

Exponential

c)

Neither

30.

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

a)

Growth

b)

Decay

c)

Linear

d)

None

31.

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

a)

Growth

b)

Decay

c)

Linear

d)

None

32.

What is the y-intercept of the function?

a)

2

b)

3

c)

1

d)

-2

33.

Identify the y-intercept (initial value) in the function f(x)=13(.27)^x

a)

(.27)^x

b)

.27

c)

13

d)

3.51

34.

Identify the y-intercept (initial value) of the function f(x)=2(4)^x.

a)

2

b)

4

c)

(2)^x

d)

8

35.

In an exponential function, what does the 'a' represent?

a)

SLOPE

b)

RATE OF CHANGE

c)

Y-INTERCEPT

d)

COMMON RATIO

36.

Is the following function and example of decay or growth?

f(x)=2(0.85)^x

a)

Exponential Decay

b)

Exponential Growth

37.

What is the common ratio(multiplier) for the sequence:

3, 15, 75...

a)

12

b)

1/5

c)

5

38.

How do you write 5% as a decimal?

a)

50

b)

5

c)

0.5

d)

0.05

39.

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

a)

300

b)

1.16

c)

.16

d)

x

40.

$10^3=$

a)

$10\times10\times10$

b)

$10\times3$

c)

$10+10+10$

d)

10,000

41.

If a number or variable does not have an exponent, we can assume the exponent is:

a)

0

b)

1

42.

$y^0=$

a)

y

b)

0

c)

1

d)

10

43.

$365^0=$

a)

0

b)

1

c)

365

d)

$\frac{1}{365}$

44.

$x^{-5}$ =

a)

$\frac{1}{x^{-5}}$

b)

$\frac{1}{x^5}$

c)

$\frac{x^5}{1}$

d)

$\frac{x^{-5}}{1}$

45.

The product rule says that when you are multiplying two exponents with the same base, you keep the base and ________ the exponents

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

46.

$x^3\cdot x^4\ =$

a)

$x^{12\ }$

b)

$x^{-1}$

c)

$x^7$

d)

$x^{34}$

47.

$m^2\cdot m^6\cdot m=$

a)

$m^8$

b)

$m^{12}$

c)

$m^4$

d)

$m^9$

48.

The quotient rule says that when you are dividing two exponents with the same base, you keep the base and __________ the exponents.

a)

Add

b)

Subract

c)

Multiply

d)

Divide

49.

$\frac{x^9}{x^4}$ =

a)

$x^{13}$

b)

$x^{36}$

c)

$x^5$

d)

$x^{-5}$

50.

$\frac{x^{17}}{x^8}$

a)

$x^9$

b)

$x^{25}$

c)

$x^{-9}$

d)

$x^{-25}$

51.

$\frac{9x^2}{3x^{ }}=$

a)

$3x^2$

b)

$3x$

c)

$9x$

d)

$6x$

52.

$\frac{a^5b^{10}}{a^3b^6}=$

a)

$a^8b^{16}$

b)

$a^2b^4$

c)

$a^{15}b^{60}$

d)

$a^2b^{16}$

53.

$\left(x^5\right)^4$

The power of a power rule says that when an exponential expression is raised to a power (as shown above), you should _________ the inner and outer exponents

a)

add

b)

subtract

c)

multiply

d)

divide

54.

$\left(x^7\right)^2$ =

a)

$x^{14}$

b)

$x^9$

c)

$x^5$

d)

$2x^7$

55.

$\left(a^3b^5\right)^7$ =

a)

$a^3b^{35}$

b)

$a^{10}b^{12}$

c)

$a^8b^8$

d)

$a^{21}b^{35}$

56.

$\left(ab^2\right)^8$ =

a)

$ab^{16}$

b)

$a^8b^{16}$

c)

$a^9b^{10}$

d)

$ab^{10}$

Unit 2- Exponents Review

Total questions: 56

Worksheet time: 2hrs 27mins

Similar Resources on Wayground