Question 1

What is the domain of 
  ?

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 ...

Question 2

Find the domain and asymptotes of the function

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Question 3

Find the domain of the function 
  
.

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...

Question 4

The hydrogen ion concentration [H⁺] for a certain substance is 0.000316. What is the pH of the substance?

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Question 5

If the equation   is converted to the form  , then a = _____ and k = _____. Give k to 4 decimal places.

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Question 6

Let   , with t measured in years. What is the continuous percent decay rate per year?

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Question 7

Let   , with t measured in years. What is the percent annual growth rate? Round to 2 decimal places.

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Question 8

The doubling time for a bank account that is growing by 3.1% per year (compounded continually) is _____ years. Round 1 decimal place.

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Question 9

If   is converted to the form  , then b = _____. Round to 3 decimal places.

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Question 10

What is the half-life of a substance that decays at a rate of 3.27% per week? Round your answer to the nearest hundredth of a week.

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Question 11

What annual interest rate, compounded monthly, is equivalent to an annual interest rate of 5.9% compounded continuously? Round your answer to the nearest thousandth of a percent, if necessary.

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Question 12

You invest $5000 in an account earning 5% annual interest. At the same time, you invest $  in a different account earning  % annual interest. In both accounts, the interest is compounded continuously. When do the accounts each hold the same amount? Round your answer to the nearest year.

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Question 13

A small country is experiencing hyperinflation of 59% per month.
A) By what percent have prices climbed after 5 months?
B) If an item currently costs $12, how much will it cost after 1 year of such inflation?

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Question 14

Suppose the population of an endangered species is cut in half every 55 years. Assume exponential decay.
A) What is the annual growth rate?
B) What is the continuous growth rate?
Give your answers correct to 4 decimal places.

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Question 15

If 14% of a radioactive substance decays in 7 hours, what is the half-life of the substance? Round your answer to 3 decimal places.

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Question 16

If 11% of a radioactive substance decays in 7 hours, what percent of the substance is left after 10 hours? Round your answer to 3 decimal places, if necessary.

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Question 17

The half-life of a substance is 36 hours. If there are initially 100 grams of the substance, write a formula to determine the amount Q remaining after t hours.

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Question 18

The half-life of a substance is 39 hours. If there are initially 110 grams of the substance, how many grams are remaining after 48 hours? Round your answer to 3 decimal places.

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Question 19

A town with an initial population of 11,000 people doubles every 40 years. Write an equation to determine the town's population P after t years.

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Question 20

A town with an initial population of 13,000 people doubles every 41 years. Determine the town's population after 9 years.

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Quiz 5: Logarithmic Functions

What is the domain of ?

Find the domain and asymptotes of the function

Find the domain of the function .

The hydrogen ion concentration [H⁺] for a certain substance is 0.000316. What is the pH of the substance?

If the equation is converted to the form , then a = _ and k = _. Give k to 4 decimal places.

Let , with t measured in years. What is the continuous percent decay rate per year?

Let , with t measured in years. What is the percent annual growth rate? Round to 2 decimal places.

The doubling time for a bank account that is growing by 3.1% per year (compounded continually) is _____ years. Round 1 decimal place.

If is converted to the form , then b = _____. Round to 3 decimal places.

What is the half-life of a substance that decays at a rate of 3.27% per week? Round your answer to the nearest hundredth of a week.

What annual interest rate, compounded monthly, is equivalent to an annual interest rate of 5.9% compounded continuously? Round your answer to the nearest thousandth of a percent, if necessary.

You invest $5000 in an account earning 5% annual interest. At the same time, you invest $ in a different account earning % annual interest. In both accounts, the interest is compounded continuously. When do the accounts each hold the same amount? Round your answer to the nearest year.

A small country is experiencing hyperinflation of 59% per month. A) By what percent have prices climbed after 5 months? B) If an item currently costs $12, how much will it cost after 1 year of such inflation?

Suppose the population of an endangered species is cut in half every 55 years. Assume exponential decay. A) What is the annual growth rate? B) What is the continuous growth rate? Give your answers correct to 4 decimal places.

If 14% of a radioactive substance decays in 7 hours, what is the half-life of the substance? Round your answer to 3 decimal places.

If 11% of a radioactive substance decays in 7 hours, what percent of the substance is left after 10 hours? Round your answer to 3 decimal places, if necessary.

The half-life of a substance is 36 hours. If there are initially 100 grams of the substance, write a formula to determine the amount Q remaining after t hours.

The half-life of a substance is 39 hours. If there are initially 110 grams of the substance, how many grams are remaining after 48 hours? Round your answer to 3 decimal places.

A town with an initial population of 11,000 people doubles every 40 years. Write an equation to determine the town's population P after t years.

A town with an initial population of 13,000 people doubles every 41 years. Determine the town's population after 9 years.

Quiz 5: Logarithmic Functions

What is the domain of ?

Find the domain and asymptotes of the function

Find the domain of the function .

The hydrogen ion concentration [H+] for a certain substance is 0.000316. What is the pH of the substance?

If the equation is converted to the form , then a = _____ and k = _____. Give k to 4 decimal places.

Let , with t measured in years. What is the continuous percent decay rate per year?

Let , with t measured in years. What is the percent annual growth rate? Round to 2 decimal places.

The doubling time for a bank account that is growing by 3.1% per year (compounded continually) is _____ years. Round 1 decimal place.

If is converted to the form , then b = _____. Round to 3 decimal places.

What is the half-life of a substance that decays at a rate of 3.27% per week? Round your answer to the nearest hundredth of a week.

What annual interest rate, compounded monthly, is equivalent to an annual interest rate of 5.9% compounded continuously? Round your answer to the nearest thousandth of a percent, if necessary.

You invest $5000 in an account earning 5% annual interest. At the same time, you invest $ in a different account earning % annual interest. In both accounts, the interest is compounded continuously. When do the accounts each hold the same amount? Round your answer to the nearest year.

A small country is experiencing hyperinflation of 59% per month. A) By what percent have prices climbed after 5 months? B) If an item currently costs $12, how much will it cost after 1 year of such inflation?

Suppose the population of an endangered species is cut in half every 55 years. Assume exponential decay. A) What is the annual growth rate? B) What is the continuous growth rate? Give your answers correct to 4 decimal places.

If 14% of a radioactive substance decays in 7 hours, what is the half-life of the substance? Round your answer to 3 decimal places.

If 11% of a radioactive substance decays in 7 hours, what percent of the substance is left after 10 hours? Round your answer to 3 decimal places, if necessary.

The half-life of a substance is 36 hours. If there are initially 100 grams of the substance, write a formula to determine the amount Q remaining after t hours.

The half-life of a substance is 39 hours. If there are initially 110 grams of the substance, how many grams are remaining after 48 hours? Round your answer to 3 decimal places.

A town with an initial population of 11,000 people doubles every 40 years. Write an equation to determine the town's population P after t years.

A town with an initial population of 13,000 people doubles every 41 years. Determine the town's population after 9 years.

The hydrogen ion concentration [H⁺] for a certain substance is 0.000316. What is the pH of the substance?

If the equation is converted to the form , then a = _ and k = _. Give k to 4 decimal places.