Free Printable Exponential & Logarithmic Functions

1.

What is the equation that represents the exponential function in the image below?

a)

y=3(½)^x

b)

y=3(2)^x

c)

y=(2)^x

d)

y=2(3)^x

2.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

3.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

4.

log₅25 = ?

a)

2

b)

5

c)

25

d)

125

5.

Evaluate log₅20 to the third decimal place

a)

0.537

b)

2.996

c)

1.301

d)

1.861

6.

Solve: 9^8-x = 27^x-3

a)

5

b)

-5

c)

1/5

d)

-1/5

7.

Solve the following for 'x';
log₆(3x - 2) = log₆(5x - 8)

a)

x = 3

b)

x = 2

c)

x = -1

d)

No Solution

8.

Use multiple log properties to write as a single log:
log₂x - 5log₂y

a)

log₂(x/y⁵)

b)

log₂(xy⁵)

c)

log₂(x/y)⁵

d)

log₂(x/5y)

9.

A sum of $1000 is invested at an interest rate of 12% per year. Find the amount of in the account after 3 years if interest is compounded daily.

a)

$1404.93

b)

$1425.76

c)

$1430.77

d)

$1433.24

10.

Solve the following equation:

3 log (2x) = 16

a)

x = 2.667

b)

x = .7699

c)

x = 107,721.734

d)

x = 4096

11.

A town doubles its size every year. If the population is currently 6,000, what will the population be in 13 years?

a)

3,990,849

b)

49,152,000

c)

698,794

d)

23,456,781

12.

Change 6.75% to a decimal.

a)

67.5

b)

.675

c)

675

d)

.0675

13.

Chelsea put $7500 into an account paying 5% compounded continuously. How much money will she have after 4 years?

a)

$9,160.52

b)

$9,116.30

c)

$7,882.09

d)

$9,720.00

14.

How much money invested at 3.45% compounded continuously for 5 years will yield $8,750?

a)

$1,559.01

b)

$10,367.18

c)

$10,397.38

d)

$7,363.64

15.

Suppose an automobile that originally costs $14,000 was to INCREASE its value by 20% every year.

What exponential equation can we create to model this situation?

a)

y=14000(.20)^x

b)

y=14000(.80)^x

c)

y=14000(1.20)^x

d)

y=14000(1.80)^x

16.

Most automobiles depreciate as they get older. Suppose an automobile that originally costs $14,000 depreciates by 20% of its value every year.

What exponential equation can we create to model this situation?

a)

y=14000(.20)^x

b)

y=14000(.80)^x

c)

y=14000(1.20)^x

d)

y=14000(1.80)^x

17.

The amount of money in an account at any given time is modeled by the equation A = 4100(1.45)^x. How does the amount of money in the account change each year?

a)

It increases by 145%.

b)

It increases by 45%.

c)

It decreases by 145%.

d)

In decreases by 45%.

18.

Find the average rate of change over the given interval.

a)

4

b)

7

c)

7/3

d)

3/7

19.

Describe the transformations that change the graph of $f\left(x\right)=\ln\left(x\right)$ to the graph of $g\left(x\right)=\ln\left(x-1\right)+4$

a)

Left 1, Up 4

b)

Right 1, Down 4

c)

Left 1, Down 4

d)

Right 1, Up 4

20.

Describe the transformations that change the graph of $y=2^x$ to the graph of $y=2^{x+4}+5$

a)

Left 4, Up 5

b)

Right 4, Up 5

c)

Left 4, Down 5

d)

Right 4, Down 5

21.

Solve

a)

A

b)

B

c)

C

d)

D

22.

According to fish and game experts, the population of salmon in the United States in March 2010 was about 6 million and growing exponentially. By the end of the year, the population had grown to 7.127 million. The projected U.S. salmon population (in millions) x years after 2010 is given by the following function: $f\left(x\right)=7.127e^{.217x}$ .

In what year did the population of fish reach 60 million?

a)

2017

b)

2018

c)

2019

d)

2020

23.

According to fish and game experts, the population of salmon in the United States in March 2010 was about 6 million and growing exponentially. By the end of the year, the population had grown to 7.127 million. The projected U.S. salmon population (in millions) x years after 2010 is given by the following function: $f\left(x\right)=7.127e^{.217x}$ .
What was the fish population in 2015?

a)

21.09 million

b)

184.73 million

c)

42.78 million

d)

96.72 million

Exponential & Logarithmic Functions

Total questions: 23

Worksheet time: 4hrs 34mins

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