Question 1

In 2002 the population of Stony Creek was 6500. Their population increases by 0.5% per year. What is the expected population in Stony Creek in 2009? Round your answer to the nearest whole number.
A) 6732
B) 215,250
C) 6533
D) 232

Accepted Answer

The population increases by 0.5% per year, so the formula for population growth is P = 6500 * (1 + 0.005)^(2009-2002). Calculating this gives approximately 6732.

Question 2

In 2001, the population of Pleasantville was 53,500. Their population increases by 2.6% per year. What is the expected population of Pleasantville in 2018? Round your answer to the nearest whole number.
A) 126,176
B) 54,891
C) 83,236
D) 29,736

Accepted Answer

The population grows exponentially, calculated as 53,500 * (1 + 0.026)^(2018-2001), which equals approximately 83,236.

Question 3

In 2001 the population of Mountainville was 9,800. Their population increases by 0.24% per year. What is the expected population of Mountainville in 2007? Round your answer to the nearest whole number.

Accepted Answer

9,942

Question 4

Phytoplankton are microscopic plants that live in the ocean. Phytoplankton grow abundantly in oceans around the world and are the foundation of the marine food chain. One variety of phytoplankton growing in Arctic waters is increasing at a rate of 17% per month. If it is estimated that there are 80 million in the water, how many will there be in 8 months? Utilize formula  where N represents the population of phytoplankton. Round to the nearest million.
A) 1833 millions
B) 312 millions
C) 10,880 millions
D) 1510 millions

Accepted Answer

The answer of Phytoplankton are microscopic plants that live in...

Question 5

An cherry pie is taken out of the oven with an internal temperature of 338°F. It is placed on a rack in a room with a temperature of 78°F. After 18 minutes, the temperature of the pie is 225°F. What will be the temperature of the pie 20 minutes after coming out of the oven? Round to one decimal place.
A) 216.0°F
B) 215.1°F
C) 567.9°F
D) 343.6°F

Accepted Answer

The temperature of the pie is decreasing exponentially. The rate of decrease is proportional to the difference between the temperature of the pie and the temperature of the room. After 18 minutes, the temperature of the pie is 225°F. This means that the temperature of the pie has decreased by 338°F - 225°F = 113°F. The rate of decrease is therefore 113°F / 18 minutes = 6.33°F per minute. After 20 minutes, the temperature of the pie will have decreased by 6.33°F per minute * 20 minutes = 126.6°F. Therefore, the temperature of the pie will be 225°F - 126.6°F = 216.0°F.

Question 6

At 1 P.M. a body is found in a park. The police measure the body's temperature to be 84°F. At  . the medical examiner arrives and determines the temperature to be 80°F. Assuming the temperature of the park was constant at 59°F, how long has the victim been dead? (Normal body temperature is 98.6°F.) Round to one decimal place.
A) 10.6 hours before 5 P.M.
B) 4.6 hours before 1 P.M.
C) 10.6 hours before 1 P.M.
D) 24.3 hours before 1 P.M.

Accepted Answer

The answer of At 1 P.M. a body is found...

Question 7

Carbon-14 has a half-life of 5730 years. How long will it take 15 grams of carbon-14 to be reduced to 12.5 grams? Round to the nearest year.
A) 655 years
B) 3470 years
C) 1507 years
D) 14,812 years

Accepted Answer

The decay of carbon-14 follows an exponential decay model. Using the formula for half-life decay, it takes approximately 5730 years for the amount to reduce by half. To reduce from 15 grams to 12.5 grams, which is a reduction by 1/8, it takes about 1507 years.

Question 8

Victor just graduated from law school owing $75,000 in student loans. The annual interest rate is 8.5%. Approximately how many years will it take to pay off her student loan if she makes a monthly payment of $690? Round to the nearest year.

Accepted Answer

The answer of Victor just graduated from law school owing...

Question 9

Match the function with the graph and the model name.

A) Logistic

B) Logistic

C) Logistic

D) Logistic

Accepted Answer

The answer of Match the function with the graph and...

Question 10

Match the graph and the model name with the function.
Exponential decay

A) 
B) 
C) 
D)

Accepted Answer

The answer of Match the graph and the model name...

Question 11

Does the graph shown display exponential growth or decay?

Accepted Answer

The answer of Does the graph shown display exponential growth...

Question 12

Find the time it will take to pay off a credit card with a balance of $12,300.00 and interest rate of 13.1% if the monthly payment is $450. Express the answer as years to the nearest 2 decimal places.

Accepted Answer

The answer of Find the time it will take to...

Question 13

Solve the exponential equation exactly for x. 
A) 3/2
B) 217/2
C) 1
D) 2

Accepted Answer

The answer of Solve the exponential equation exactly for x....

Question 14

Solve the exponential equation exactly for x. 
A) 1/2
B) 2
C) 5
D) 1/5

Accepted Answer

The answer of Solve the exponential equation exactly for x....

Question 15

Solve the exponential equation exactly for x.

A) -2
B) 1
C) 3
D) -1

Accepted Answer

The answer of Solve the exponential equation exactly for x.

A)...

Question 16

Solve the exponential equation exactly for x.

A) 2
B) -4
C) 4
D) 2, -2

Accepted Answer

The answer of Solve the exponential equation exactly for x.

A)...

Question 17

Solve the exponential equation exactly for x. 
A) -4
B) -4, 4
C) 2
D) -2, 2

Accepted Answer

The answer of Solve the exponential equation exactly for x....

Question 18

Solve the exponential equation. Round your answer to two decimal places. 
A) 1.00
B) 1.08
C) 2.80
D) 0.71

Accepted Answer

The answer of Solve the exponential equation. Round your answer...

Question 19

Solve the exponential equation. Round your answer to two decimal places. 
A) 0.90
B) 0.78
C) 3.50
D) 0.34

Accepted Answer

The answer of Solve the exponential equation. Round your answer...

Question 20

Solve the logarithmic equation exactly. 
A) 5.5
B) 7
C) 22
D) 6

Accepted Answer

The answer of Solve the logarithmic equation exactly. 
A) 5.5
B)...

Quiz 5: Exponential and Logarithmic Functions

In 2002 the population of Stony Creek was 6500. Their population increases by 0.5% per year. What is the expected population in Stony Creek in 2009? Round your answer to the nearest whole number.

In 2001, the population of Pleasantville was 53,500. Their population increases by 2.6% per year. What is the expected population of Pleasantville in 2018? Round your answer to the nearest whole number.

In 2001 the population of Mountainville was 9,800. Their population increases by 0.24% per year. What is the expected population of Mountainville in 2007? Round your answer to the nearest whole number.

Carbon-14 has a half-life of 5730 years. How long will it take 15 grams of carbon-14 to be reduced to 12.5 grams? Round to the nearest year.

Victor just graduated from law school owing $75,000 in student loans. The annual interest rate is 8.5%. Approximately how many years will it take to pay off her student loan if she makes a monthly payment of $690? Round to the nearest year.

Match the function with the graph and the model name.

Match the graph and the model name with the function. Exponential decay

Does the graph shown display exponential growth or decay?

Find the time it will take to pay off a credit card with a balance of $12,300.00 and interest rate of 13.1% if the monthly payment is $450. Express the answer as years to the nearest 2 decimal places.

Solve the exponential equation exactly for x.

Solve the exponential equation exactly for x.

Solve the exponential equation exactly for x.

Solve the exponential equation exactly for x.

Solve the exponential equation exactly for x.

Solve the exponential equation. Round your answer to two decimal places.

Solve the exponential equation. Round your answer to two decimal places.

Solve the logarithmic equation exactly.