Free Printable Algebra 1: Topic 6 (Exponents & Exponential Functions)

1.

Which option is exponential growth?

a)

Option 1

b)

Option 2

2.

Simplify (7x⁴)(9x³)

a)

16x¹²

b)

16 x⁷

c)

63x⁴⁺³ = 63x⁷

d)

63x^4*3= 63x¹²

3.

How would you change this to a positive exponent:
1/x^-3

a)

1/x³

b)

x³

c)

3x

d)

1/3x

4.

What should you do with the exponents in order to simplify this expression?
(c⁵)(c³)(c³)

a)

Subtract them

b)

Multiply them

c)

Add them

d)

Divide them

5.

Rewrite in Exponential Form.

a)

A

b)

B

c)

C

d)

D

6.

a)

$g\left(x\right)=6\left(\frac{1}{3}\right)^{x\ }$

b)

$g\left(x\right)=6\left(3\right)^x$

c)

$g\left(x\right)=6-\left(\frac{1}{3}\right)^{x\ }$

d)

$g\left(x\right)=6-\left(3\right)^x$

7.

a)

$f\left(x\right)=15\left(\frac{5}{6}\right)^x$

b)

$f\left(x\right)=18\left(\frac{6}{5}\right)^x$

c)

$f\left(x\right)=15\left(\frac{6}{5}\right)^x$

d)

$f\left(x\right)=18\left(\frac{5}{6}\right)^x$

8.

Determine which type of function best models the data in the table. Support your answer.

a)

exponential

b)

linear

c)

Neither

d)

It has a common difference of 4

e)

It has a common multiplier of 3

9.

Rewrite the expression without using a radical:

a)

(x - 1)^3/4

b)

(x - 1)^4/3

c)

3(x - 1)⁴

d)

4(x - 1)³

10.

8

a)

W

b)

O

c)

R

d)

K

11.

Solve the equation

2^{\left(x+1\right)}=2^5

(a)

12.

Solve the equation

3^{\left(x-1\right)}=9

(a)

13.

Solve the equation

4^2=8^x

(a)

14.

find x.

a)

-3

b)

-2

c)

1/3

d)

2

e)

3

15.

When dividing numbers with the same base, you have to _____ the exponents.

a)

multiply

b)

subtract

c)

divide

d)

add

16.

Which of the following is TRUE?

a)

$8^{\frac{1}{2}}+8^{\frac{1}{3}}=8^5$

b)

$\frac{3^{\frac{1}{4}}}{3^{\frac{1}{5}}}=3^{\frac{2}{9}}$

c)

$\left(3^{\frac{1}{3}}\right)^2=3^{\frac{2}{6}}$

d)

$4^{-2}=\frac{1}{16}$

17.

To earn as much interest as possible, you should open a savings account that earns ______ interest and has the _____ interest rate.

a)

compound; lowest

b)

simple ; lowest

c)

compound ; highest

d)

simple ; highest

18.

Find the compound interest:
Principal: $1735
Interest Rate: 0.8%
Time: 1 year

a)

$1,388

b)

$138.80

c)

$13.88

d)

None of the answers are correct.

19.

Find the simple interest:
Principal: $6,000
Interest Rate: 5%
Time: 6 months

a)

$150

b)

$1,800

c)

$1,500

d)

$15,000

20.

Semi-Annually means how many times a year?

a)

4

b)

2

c)

1

d)

6

21.

Courtney saved up $2,200 working as a waitress over the summer. She put this money into a bank account that earned 5.2% interest and is compounded daily. How much will she have in her account at the end of 4 years?

a)

$2201.25

b)

$2694.55

c)

$2707.45

d)

$2708.63

22.

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 interest will she earn in 10 years?

a)

$915.59

b)

$933.28

c)

$979.81

d)

$1,005.09

23.

Write the following expression in radical form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

24.

a)

5x^5/4

b)

5x^-5/4

c)

(5x)^-5/4

d)

(5x)^-4/5

25.

What is the cube root of 1000?

a)

10

b)

100

c)

500

d)

20

26.

What is the cube root of 8?

a)

4

b)

2

c)

-2

d)

-4

27.

Evaluate without a calculator.

a)

A

b)

B

c)

C

d)

D

28.

Is $\left(-3\right)^2$ the same thing as $-3^2$ ?

a)

Yes

b)

No

29.

Is $8^3$ the same thing as $8\times3$ ?

a)

Yes

b)

No

30.

$x^0=$

a)

0

b)

1

c)

x

d)

-x

31.

Select all the expressions that are equivalent to $4^{-3}$ .

a)

$-12$

b)

$\frac{1}{64}$

c)

$-64$

d)

$\frac{1}{4^3}$

e)

$64$

32.

Is this exponential growth or decay?

a)

Growth

b)

Decay

33.

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

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None of the above

34.

What is the base in
f(x)=2(6)^x+3-8 ?

a)

2

b)

6

c)

-3

d)

-8

35.

Using the parent function y=3^x what would the graph of y=3^x+1 look like?

a)

Horizontal shift left one unit!

b)

Horizontal shift right one unit!

c)

Vertical shift up one unit!

d)

Vertical shift down one unit!

36.

Using the parent function y=3^x what would the graph of y=3^x+1 look like?

a)

Horizontal Shift to the right 1 unit

b)

Horizontal shift to the left one unit

c)

Vertical shift one unit up

d)

Vertical shift one unit down

37.

Describe the transformations for the following function:

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

a)

2 units right and 4 units up

b)

4 units to the left and 2 units up

c)

2 unit right and 4 units down

d)

2 units left and 4 units down

38.

What is the horizontal asymptote for the graph of
f(x)=-2(3)^x+4-8 ?

a)

y=8

b)

y=-8

c)

x=-8

d)

x=-4

39.

What is the range of this function?

a)

(-∞,0)

b)

(0,∞)

c)

(-∞,4)

d)

(4,∞)

40.

a)

Choice A

b)

Choice B

c)

Choice C

d)

Choice D

41.

a)

Choice A

b)

Choice B

c)

Choice C

d)

Choice D

42.

Which function is exponential?

a)

f(x)

b)

h(x)

c)

g(x)

43.

Use the function, M=.05(2)^t, where M is the amount of money you have after t days.
How much money will you have after 14 days?

a)

$ 819.20

b)

$ 8,192.00

c)

$ 1.40

d)

$ 819.02

44.

Use the function, N = 14,000(.96)^t. Where N is the number of employees and t is the number of years.
How many employees will there be after 3 years?

a)

14,000 employees

b)

12,386 employees

c)

40,360 employees

d)

15,748 employees

45.

h(x)= 12^{x
Find h(-2)}

a)

1/144

b)

1/24

c)

-144

d)

-24

46.

What type of function describes the story below?
You have $5 and triple your money every day.

a)

Linear

b)

Exponential

c)

Neither

47.

Determine if the table represents linear or Exponential Function.

a)

Linear

b)

Exponential

c)

Neither

48.

What is the asymptote of the graph?

a)

x=2

b)

y=-2

c)

y=0

d)

y=-1

49.

What is the asymptote?

a)

y=0

b)

x=2

c)

y=1

d)

x=0

50.

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

51.

What is the asymptote value in the function?

a)

y = 3

b)

y = 2

c)

y = 7

d)

y = 0

52.

Write the equation of the graph.

a)

f(x) = -3^x- 2

b)

f(x) = -3^x + 2

c)

f(x) = 3^x + 2

d)

f(x) = 3^-x + 2

Algebra 1: Topic 6 (Exponents & Exponential Functions)

Total questions: 52

Worksheet time: 2hrs 36mins

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