Quiz about Exponential & Logarithmic Functions

Question 1

Write in exponential form.
log₂32 = 5

Accepted Answer

25 = 32

Answer

2-5 = 32

Answer

232 = 5

Answer

325 = 2

Question 2

Rewrite 3⁴ = 81 in logarithmic form.

Accepted Answer

log₃81 = 4

Answer

log₃4 = 81

Answer

log₈₁3 = 4

Answer

log₄81 = 3

Question 3

log₅25 = ?

Accepted Answer

2

Answer

5

Answer

25

Answer

125

Question 4

Evaluate log₅20 to the third decimal place

Accepted Answer

1.861

Answer

0.537

Answer

2.996

Answer

1.301

Question 5

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

Accepted Answer

5

Answer

-5

Answer

1/5

Answer

-1/5

Question 6

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

Accepted Answer

x = 3

Answer

x = 2

Answer

x = -1

Answer

No Solution

Question 7

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

Accepted Answer

log₂(x/y⁵)

Answer

log₂(xy⁵)

Answer

log₂(x/y)⁵

Answer

log₂(x/5y)

Question 8

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.

Accepted Answer

$1433.24

Answer

$1404.93

Answer

$1425.76

Answer

$1430.77

Question 9

Solve the following equation:

3 log (2x) = 16

Accepted Answer

x = 107,721.734

Answer

x = 2.667

Answer

x = .7699

Answer

x = 4096

Question 10

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

Accepted Answer

49,152,000

Answer

3,990,849

Answer

698,794

Answer

23,456,781

Question 11

Change 6.75% to a decimal.

Accepted Answer

.0675

Answer

67.5

Answer

.675

Answer

675

Question 12

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

Accepted Answer

$9,160.52

Answer

$9,116.30

Answer

$7,882.09

Answer

$9,720.00

Question 13

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

Accepted Answer

$7,363.64

Answer

$1,559.01

Answer

$10,367.18

Answer

$10,397.38

Question 14

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?

Accepted Answer

y=14000(1.20)^x

Answer

y=14000(.20)^x

Answer

y=14000(.80)^x

Answer

y=14000(1.80)^x

Question 15

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?

Accepted Answer

y=14000(.80)^x

Answer

y=14000(.20)^x

Answer

y=14000(1.20)^x

Answer

y=14000(1.80)^x

Question 16

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?

Accepted Answer

It increases by 45%.

Answer

It increases by 145%.

Answer

It decreases by 145%.

Answer

In decreases by 45%.

Question 17

Find the average rate of change over the given interval.

Accepted Answer

7/3

Answer

4

Answer

7

Answer

3/7

Question 18

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

Accepted Answer

Left 4, Up 5

Answer

Right 4, Up 5

Answer

Left 4, Down 5

Answer

Right 4, Down 5

Question 19

Solve

Accepted Answer

B

Answer

A

Answer

C

Answer

D

Question 20

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: $y=2^x$ .

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

Accepted Answer

2019

Answer

2017

Answer

2018

Answer

2020

Question 21

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: $y=2^x$ .
What was the fish population in 2015?

Accepted Answer

21.09 million

Answer

184.73 million

Answer

42.78 million

Answer

96.72 million

Exponential & Logarithmic Functions

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