Free Printable Exponents and Exponential Functions

1.

Agnes purchases a ring for $200 and it depreciates 6% per year from the date of purchase. Which function models the value V(t) of the ring?

a)

V(t)=200(1.6)^t

b)

V(t)=1.06x+200

c)

V(t)=200(.06)^t

d)

V(t)=200(.94)^t

2.

Which option is exponential growth?

a)

Option 1

b)

Option 2

3.

The equation y = 75(1.2)^x describes the number of staff since 1998.
What 'x' would you use if you wanted to calculate the number of staff in 2005?

a)

x = 2005

b)

x = 7

c)

x = 5

d)

x = 1998

4.

USE THE CALCULATOR:
The equation y = 75(1.2)^x describes the number of staff since 1998.
What is an approximate number of staff in the year 2005?

a)

269

b)

187

5.

Which equation shows
"The cell population of 200 is growing by 20 percent each hour"?

a)

P(h) = 200 (.20)^h

b)

P(h) = 200 (20)^h

c)

P(h) = 200 (1.20)^h

d)

P(h) = 200 (.80)^h

6.

Which equation shows
"The cell population of 200 is reducing by 20 percent each hour"?

a)

P(h) = 200 (.20)^h

b)

P(h) = 200 (20)^h

c)

P(h) = 200 (1.20)^h

d)

P(h) = 200 (.80)^h

7.

The value of an investment is modeled by the function y = 125 (1.4)^x. Which statement is true

a)

The value of the investment will increase over time

b)

The value of the investment will decrease over time

c)

The value of the investment will remain the same

8.

Simplify (7x⁴)(9x³)

a)

16x¹²

b)

16 x⁷

c)

63x⁴⁺³ = 63x⁷

d)

63x^4*3= 63x¹²

9.

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

a)

1/x³

b)

x³

c)

3x

d)

1/3x

10.

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

11.

Simplify
(c⁵)(c³)(c^-³)

a)

c⁵

b)

3c¹¹

c)

c¹¹

d)

3c⁴⁵

12.

Simplify:

a)

A

b)

B

c)

C

d)

D

13.

Simplify
(2xy⁵)(-3x²y⁷)

a)

-6x²y¹²

b)

-1x²y¹²

c)

-5x²y³⁵

d)

-6x³y¹²

14.

Simplify.

a)

y^-4

b)

¹/_y¹⁶

c)

y^-16

d)

y⁴

15.

a)

a

b)

b

c)

c

d)

d

16.

Rewrite in Exponential Form.

a)

A

b)

B

c)

C

d)

D

17.

Simplify
10x²y⁰

a)

1

b)

10x²y

c)

10x²

d)

x²

18.

Find the equivalent expression.

(-9)(-9)(-9)(-9)(-9)

a)

-9⁵

b)

(-9)⁵

c)

-9 x 5

d)

-9 + -9 + -9 + -9+ -9

19.

Simplify.

(3x³y⁵)⁴

a)

3x⁷y⁹

b)

81x¹²y²⁰

c)

12x¹²y²⁰

d)

81x⁷y⁹

20.

Simplify.

(45x⁶y²)/(5x⁴y⁹)

a)

9x²/y⁷

b)

40x²y⁷

c)

9x²y⁷

d)

9x¹⁰y¹¹

21.

Evaluate this expression using the quotient rule. Leave your answer in exponent form.

a)

9⁵

b)

9⁹

c)

1⁵

d)

9^-5

22.

(7uv²)^-5

a)

-35uv^-10

b)

-5/7uv²

c)

1/16807u⁵v¹⁰

d)

-16807/u⁵v¹⁰

23.

Simplify (-4r⁵)(2r⁸)

a)

-8r¹³

b)

-2r¹³

c)

-8r⁴⁰

d)

-2y⁴⁰

24.

You deposit $1250 in an investment account earning 12% interest. How much money will you have in 15 years?

a)

1926

b)

6841.96

c)

6397.61

d)

1400

25.

a)

2a²b⁶

b)

1/2a²b⁶

c)

b⁶/2a²

d)

2b⁶/a²

26.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same

d)

Zero is greater

27.

You purchased a car for $35,000 and the value of the car depreciates at a rate of 9% each year. What is the value of the car after 8 years?

a)

$16,459.84

b)

$69,739.69

c)

$15,066

d)

$31,850

28.

What is the y-intercept of the function?

a)

2

b)

3

c)

1

d)

-2

29.

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

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None

30.

What is the initial value of the function y=⅓ × 4^x

a)

⅓

b)

3

c)

4

d)

¼

31.

There are 5 original students that started at Texas Tech in 1923, each year the campus grew triple the size of the previous year, whats the function?

a)

y=(1/3)5^x

b)

y=5(1/3)^x

c)

y=5(3)^x

d)

y=3(5)^x

32.

What is the domain of the function shown below?

a)

-2 < x < 5

b)

0 < x < 12

c)

y > 0

d)

All Real Numbers

33.

What is the range of this graph?

a)

y = 6

b)

(0, -4)

c)

y > -6

d)

y < -6

34.

What is the range of the function shown below?

a)

0 < y < 12

b)

-2 < y < 5

c)

y > 0

d)

All Real Numbers

35.

Is the pictured graph growth, decay, or linear or quadratic?

a)

Growth

b)

Decay

c)

Linear

d)

Quadratic

36.

Which represents exponential decay?

a)

A

b)

B

c)

C

d)

D

37.

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

a)

SLOPE

b)

RATE OF CHANGE

c)

Y-INTERCEPT

d)

COMMON RATIO

38.

Write the following expression in radical form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

39.

Write the following expression in radical form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

40.

Write the following expression in exponential form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

41.

Write the following expression in radical form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

42.

Simplify the following expression:

a)

5

b)

25

c)

125

d)

625

43.

Simplify:

a)

2

b)

8

c)

16

d)

32

44.

Simplify:

a)

2

b)

4

c)

16

d)

64

45.

a)

7²

b)

7^1/2

c)

7^-2

d)

7^-1/2

46.

a)

2^1/6

b)

64

c)

6^1/2

d)

2⁶

47.

Re-write the expression in radical form.
x^2/3

a)

∛x²

b)

√x³

c)

(1/x)

d)

∛x

48.

8

a)

W

b)

O

c)

R

d)

K

49.

$yx^{\frac{1}{3}}\cdot xy^{\frac{3}{2}}$

a)

$x^{\frac{4}{3}}y^{\frac{5}{2}}$

b)

$x^{\frac{2}{3}}y^{\frac{1}{2}}$

c)

$x^{\frac{1}{3}}y^{\frac{3}{2}}$

d)

$x^{\frac{2}{3}}y^{\frac{4}{3}}$

50.

Simplify . Your answer should contain only positive exponents. $4v^{\frac{2}{3}}\cdot v^{-1}$

a)

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

b)

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

c)

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

d)

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

51.

Simplify . Your answer should contain only positive exponents. $\frac{2x^{\frac{1}{2}}y^{\frac{1}{3}}}{2x^{\frac{4}{3}}y^{-\frac{7}{4}}}$

a)

$\frac{y^{\frac{25}{12}}}{x^{\frac{5}{6}}}$

b)

$\frac{x^{\frac{5}{6}}}{y^{\frac{25}{12}}}$

c)

$\frac{2y^{\frac{25}{12}}}{x^{\frac{5}{6}}}$

d)

$\frac{y^{\frac{17}{12}}}{x^{\frac{5}{6}}}$

Exponents and Exponential Functions

Total questions: 51

Worksheet time: 4hrs 15mins

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