Quiz about Exponential and Logarithmic Applications

Question 1

Expand

Accepted Answer

6log₈u-2log₈v

Answer

6log₈v-2log₈u

Answer

3log₈u-2log₈v

Answer

6log₈u+2log₈v

Question 2

Use the change of base formula and your calculator to approximate the log.

Accepted Answer

A

Answer

B

Answer

C

Answer

D

Question 3

Expand

Accepted Answer

5log₅a - 30log₅b

Answer

5log₅a - 6log₅b

Answer

5log₅a + 30log₅b

Answer

30log₅b - 5log₅a

Question 4

Expand

Accepted Answer

A

Answer

B

Answer

C

Answer

D

Question 5

Expand

Accepted Answer

C

Answer

A

Answer

B

Answer

D

Question 6

Expand the logarithm.

Accepted Answer

C

Answer

A

Answer

B

Answer

D

Question 7

You have inherited land that was purchased for $30,000 in 1960. The value of the land increased by approximately 5% per year. What is the approximate value of the land in the year 2010?

Accepted Answer

$344,022

Answer

$331,500

Answer

$15,000

Answer

$28,500

Question 8

You drink a beverage with 120 mg of caffeine. Each hour, the caffeine in your system decreases by about 12%. How long until you have 10mg of caffeine?

Accepted Answer

19 to 20 hours

Answer

10 to 20 hours

Answer

15 to 16 hours

Answer

5 to 6 hours

Question 9

The foundation of your house has about 1,200 termites. The termites grow at a rate of about 2.4% per day. How long until the number of termites doubles?

Accepted Answer

29 to 30 years

Answer

23 to 24years

Answer

15 to 16 years

Answer

19 to 20 years

Question 10

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

Accepted Answer

y = 15(1.35)^x

Answer

y = 15(35)^x

Answer

y = 15(0.35)^x

Answer

y = 35(1.15)^x

Question 11

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?

Accepted Answer

9766

Answer

9006

Answer

9765

Answer

5433

Question 12

You buy a new computer for $2100. The computer decreases by 50% annually. How much is it worth after 2 years.

Accepted Answer

525

Answer

225

Answer

325

Answer

425

Question 13

Karla invested $1,000 in savings bonds. If the bonds earn 6.75% interest compounded semi-annually, how much total will Karla earn in 15 years?

Accepted Answer

$2,706.86

Answer

$1,584.62

Answer

$2,651.39

Answer

$1,825.10

Question 14

Emily would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years.

Accepted Answer

$15,683.28

Answer

$15,415.94

Answer

$15,927.56

Answer

$16,109.05

Question 15

A 78 gram sample of Uranium loses half of its mass each year.  How much is left after 6 years?

Accepted Answer

1.22 grams

Answer

13 grams

Answer

6.5 grams

Answer

592.31 grams

Question 16

During normal breathing, about 12% of the air in the lungs is replaced after one breath. Write an exponential decay model for the amount of the original air left in the lungs if the initial amount of air in the lungs is 500 mL. How much of the original air is present after 24 breaths?

Accepted Answer

23.25

Answer

22.25

Answer

24.25

Answer

25.25

Question 17

Hugo sold his car after one year for $25,000. He bought it new $29,400. What was the rate of depreciation?

Accepted Answer

15%

Answer

8%

Answer

19%

Answer

11%

Question 18

The number of farms in Indiana (in thousands) can be modeled by F = 115,000(.987)^t, where t is the number of years since 1980. According to the equation, when will the number of farms in Indiana be about 50,000?

Accepted Answer

64 years

Answer

54 years

Answer

76 years

Answer

67 years

Question 19

Halle deposited $4000 into an account that earns 5% interest each year. The growth of her investment can be expressed by the exponential equation, A = 4000(1 + .05)^t, where A is the amount in the account after t years. In how many years will her account exceed $10,000?

Accepted Answer

19 years

Answer

16 years

Answer

22 years

Answer

25 years

Question 20

The population of a small coastal resort town, currently 3400, grows at a rate of 3% per year. This growth can be expressed by the exponential equation P = 3400(1+.03)^x, where P is the population after t years. Find the number of years it will take for the population to reach 10,000?

Accepted Answer

36 years

Answer

20 years

Answer

26 years

Answer

30 years

Question 21

Halle deposited $4000 into an account that earns 5% interest each year. The growth of her investment can be expressed by the exponential equation, A = 4000(1 + .05)^t, where A is the amount in the account after t years. In how many years will her account exceed $10,000?

Accepted Answer

19 years

Answer

16 years

Answer

22 years

Answer

25 years

Question 22

Solve $$3e^x=63$$
Round your answer to the nearest 100th

Accepted Answer

Answer

Answer

Answer

Answer

none of the above

Question 23

If $1200 is put into an account that earns 3.2% interest compounded continuously, Approximately how long will the account take to have a balance of $7200?

Accepted Answer

56 years

Answer

59 years

Answer

62 years

Answer

67 years

Question 24

Convert into log form: $$e^x=5$$

Accepted Answer

Answer

$$\log_ex=5$$

Answer

$$\log_xe=5$$

Answer

$$\log e=5$$

Question 25

log₅(4x-7)=log₅(x+5)

Accepted Answer

4

Answer

3

Answer

12

Answer

7

Question 26

log₂(x + 2) + log₂x = 3

Accepted Answer

2

Answer

-4, 2

Answer

-2, 4

Answer

1

Question 27

Solve for x:
5 e^6x+3= 0.1

Accepted Answer

-1.152

Answer

0.232

Answer

-3.077

Answer

-0.854

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