Question 1

Find an exponential function,  , such that  and for every unit increase in x, the output decreases by 60 percent..
Enter your answer in  form.

Accepted Answer

The answer of Find an exponential function,  , such...

Question 2

Find an exponential function,  , such that  and for every unit increase in x, the output increases by 40 percent.. Enter your answer in  form.

Accepted Answer

The answer of Find an exponential function,  , such...

Question 3

Complete the description for the exponential function,  .
For every unit increase in the input, the output increases by ______ percent.

Accepted Answer

The answer of Complete the description for the exponential function,...

Question 4

Choose the description that best describes the exponential function,  .

Accepted Answer

The answer of Choose the description that best describes the...

Question 5

Higher education enrollment in Kentucky for the years from 1985 through 1992 is displayed in the following table.
  
Complete the sentence:
Between 1985 and 1990, the enrollment increased by A)___________ thousand students which is a B)___________ percent increase over the 5 years.
Round answers to 2 decimal places if necessary.

Accepted Answer

The answer of Higher education enrollment in Kentucky for the...

Question 6

A house valued at $65,000 in 1989 increased in value to $105,000 in 2004
A) What was the absolute change in value?
B) What was the percent change over the 15 years?
Round to 2 decimal places, if necessary.

Accepted Answer

The answer of A house valued at $65,000 in 1989...

Question 7

A house valued at $45,000 in 1989 increased in value to $140,000 in 2001
Choose the true statement.

Accepted Answer

The value of the house increased by $140,000 - $45,000 = $95,000. The percentage increase is $95,000 / $45,000 * 100% = 211%.

Question 8

In 2000, a town's population was 35,000. In 2010, the population had increased to 100,000. If the town continues to grow at the same rate (Assuming exponential growth), what will its population be in 2020?
Round your answer to the nearest thousand.

Accepted Answer

The answer of In 2000, a town's population was 35,000....

Question 9

A house valued at $45,000 in 1990 increased in value to $100,000 in 2005.
A) Find a function which gives the value of the house, V, as a function of y, the number of years after 1990.
Write your answer in  form and round values to 2 decimal places.
B) Now use that function to predict the value of the house in 2018.Round to 2 decimal places.

Accepted Answer

The answer of A house valued at $45,000 in 1990...

Question 10

In 1923, a year-old Model T automobile was purchased for $750. In 1927, it was worth $450. (Note: t = 0 in 1922).
Find a function which gives the value of the car, V, as a function of y, the number of years after 1922, assuming the value of the car depreciated...
A) Linearly. (Write your answer in  form and round values to 2 decimal places.)
B) Exponentially (Write your answer in  form and round values to 2 decimal places.)

Accepted Answer

The answer of In 1923, a year-old Model T automobile...

Question 11

The cost of college tuition increases about 3.2% each year. If the average cost of tuition is $10,500 in 2007, find a function that gives the average tuition, T, as a function of the years after 2007, y, (Write your answer in  form.)

Accepted Answer

The answer of The cost of college tuition increases about...

Question 12

The cost of college tuition increases about 3.2% each year. If the average cost of tuition is $9,500 in 2007, find:
A) a function that gives the average tuition, T, as a function of the years after 2007, y, (Write your answer in  form.) and,
B) use the function to find the average cost of tution in 2012. Round your answer to the nearest dollar.

Accepted Answer

The answer of The cost of college tuition increases about...

Question 13

What is the growth factor for an object whose mass increases by 22.7% every 3 years?

Accepted Answer

The growth factor is calculated as 1 plus the percentage increase expressed as a decimal. Since the mass increases by 22.7%, the growth factor is 1 + 0.227 = 1.227.

Question 14

What is the decay factor for a business whose profit decreases by 30.5% every 3 years?

Accepted Answer

The decay factor is calculated as 1 minus the percentage decrease expressed as a decimal. So, 1 - 0.305 = 0.695.

Question 15

A company states that their annual profit has increased by 695% over the last 12 years from 1998 to 2010. Write a function to describe the profit with f(0) being 1998 profits of $186700. Round the growth factor to 3 decimal places if necessary.

Accepted Answer

The answer of A company states that their annual profit...

Question 16

The function  represents the growth of the deer population in Wisconsin where T represents 5-year intervals. Create an equivalent function where T represents 1-year intervals. Round the growth factor to 3 decimal places.

Accepted Answer

The answer of The function  represents the growth of...

Question 17

The function  represents the decay of the Asian beetle population in Wisconsin where T represents 5-year intervals. Create an equivalent function where T represents 1-year intervals. Round the decay factor to 3 decimal places.

Accepted Answer

The answer of The function  represents the decay of...

Question 18

The following function gives the value, V, of an investment as a function of y, the years since the original investment:
  Find the doubling time.

Accepted Answer

The answer of The following function gives the value, V,...

Question 19

The following function gives the value, V, of an investment as a function of y, the years since the original investment:
  Find the doubling time to the nearest year.

Accepted Answer

The answer of The following function gives the value, V,...

Question 20

The following function gives the value, V, of an investment as a function of y, the years since the original investment:
  
Use the "Rule of 70" to estimate the doubling time to the nearest year.

Accepted Answer

The answer of The following function gives the value, V,...

Quiz 5: Growth and Decay: An Introduction to Exponential Functions

Find an exponential function, , such that and for every unit increase in x, the output decreases by 60 percent.. Enter your answer in form.

Find an exponential function, , such that and for every unit increase in x, the output increases by 40 percent.. Enter your answer in form.

Complete the description for the exponential function, . For every unit increase in the input, the output increases by ______ percent.

Choose the description that best describes the exponential function, .

A house valued at $65,000 in 1989 increased in value to $105,000 in 2004 A) What was the absolute change in value? B) What was the percent change over the 15 years? Round to 2 decimal places, if necessary.

A house valued at $45,000 in 1989 increased in value to $140,000 in 2001 Choose the true statement.

In 2000, a town's population was 35,000. In 2010, the population had increased to 100,000. If the town continues to grow at the same rate (Assuming exponential growth), what will its population be in 2020? Round your answer to the nearest thousand.

The cost of college tuition increases about 3.2% each year. If the average cost of tuition is $10,500 in 2007, find a function that gives the average tuition, T, as a function of the years after 2007, y, (Write your answer in form.)

What is the growth factor for an object whose mass increases by 22.7% every 3 years?

What is the decay factor for a business whose profit decreases by 30.5% every 3 years?

A company states that their annual profit has increased by 695% over the last 12 years from 1998 to 2010. Write a function to describe the profit with f(0) being 1998 profits of $186700. Round the growth factor to 3 decimal places if necessary.

The function represents the growth of the deer population in Wisconsin where T represents 5-year intervals. Create an equivalent function where T represents 1-year intervals. Round the growth factor to 3 decimal places.

The function represents the decay of the Asian beetle population in Wisconsin where T represents 5-year intervals. Create an equivalent function where T represents 1-year intervals. Round the decay factor to 3 decimal places.

The following function gives the value, V, of an investment as a function of y, the years since the original investment: Find the doubling time.

The following function gives the value, V, of an investment as a function of y, the years since the original investment: Find the doubling time to the nearest year.

The following function gives the value, V, of an investment as a function of y, the years since the original investment: Use the "Rule of 70" to estimate the doubling time to the nearest year.