Question 1

Solve $\log x=2$ for $x$.

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Question 2

Evaluate $10^{\log 13}$

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Question 3

Evaluate $\log \left(10^{19}\right)$

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Question 4

Evaluate $e^{\ln 9}$

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Question 5

Evaluate $\ln \left(e^{9}\right)$

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Question 6

If the equation $Q=8 \cdot 3^{1.7 t}$ is converted to the form $Q=a e^{k t}$, then $a=$----------- and $k=$ ------------- Give k to 4 decimal places.

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Question 7

Let $y=20 e^{-0.07 t}$, with $t$ measured in years. What is the continuous percent decay rate per year?

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Question 8

Let $y=60 e^{-0.07 t}$, with $t$ measured in years. What is the percent annual decay rate?
Round to 2 decimal places.

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Question 9

The doubling time for a bank account that is growing by $2.6 \%$ per year (compounded continually) is---------- years. Round 1 decimal place.

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Question 10

If $Q=\frac{1}{7} e^{0.062 t}$ is converted to the form $Q=a b^{t}$, then $b=\ldots$. Round to 3 decimal places.

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Question 11

What is the half-life of a substance that decays at a rate of $3.21 \%$ per day? Round your answer to the nearest hundredth of a day.

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Question 12

What annual interest rate, compounded monthly, is equivalent to an annual interest rate of 5.4% compounded continuously? Round your answer to the nearest thousandth of a percent, if necessary.

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Question 13

You invest $\$ 4,000$ in an account earning $4 \%$ annual interest. At the same time, you invest $\$ 8,000$ in a different account earning $2 \%$ 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 14

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 15

Suppose the population of an endangered species is cut in half every 60 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 16

If $11 \%$ of a radioactive substance decays in 8 hours, what is the half-life of the substance in hours? Round your answer to 3 decimal places.

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Question 17

If $11 \%$ of a radioactive substance decays in 6 hours, what percent of the substance is left after 11 hours? Round your answer to 3 decimal places, if necessary.

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Question 18

The half-life of a substance is 34 hours. If there are initially 125 grams of the substance, write an exponential formula to determine the amount $Q$ remaining after $t$ hours.

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Question 19

The half-life of a substance is 37 hours. If there are initially 145 grams of the substance, how many grams are remaining after 52 hours? Round your answer to 3 decimal places.

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Question 20

What is the doubling time of a population growing by $12 \%$ per year? Round your answer to the nearest hundredth of a year.

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Quiz 5: Logarithmic Functions

Solve $\log x=2$ for $x$ .

Evaluate $10^{\log 13}$

Evaluate $\log \left(10^{19}\right)$

Evaluate $e^{\ln 9}$

Evaluate $\ln \left(e^{9}\right)$

If the equation $Q=8 \cdot 3^{1.7 t}$ is converted to the form $Q=a e^{k t}$ , then $a=$ ----------- and $k=$ ------------- Give k to 4 decimal places.

Let $y=20 e^{-0.07 t}$ , with $t$ measured in years. What is the continuous percent decay rate per year?

Let $y=60 e^{-0.07 t}$ , with $t$ measured in years. What is the percent annual decay rate? Round to 2 decimal places.

The doubling time for a bank account that is growing by $2.6 \%$ per year (compounded continually) is---------- years. Round 1 decimal place.

If $Q=\frac{1}{7} e^{0.062 t}$ is converted to the form $Q=a b^{t}$ , then $b=\ldots$ . Round to 3 decimal places.

What is the half-life of a substance that decays at a rate of $3.21 \%$ per day? Round your answer to the nearest hundredth of a day.

What annual interest rate, compounded monthly, is equivalent to an annual interest rate of 5.4% compounded continuously? Round your answer to the nearest thousandth of a percent, if necessary.

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 60 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 $11 \%$ of a radioactive substance decays in 8 hours, what is the half-life of the substance in hours? Round your answer to 3 decimal places.

If $11 \%$ of a radioactive substance decays in 6 hours, what percent of the substance is left after 11 hours? Round your answer to 3 decimal places, if necessary.

The half-life of a substance is 34 hours. If there are initially 125 grams of the substance, write an exponential formula to determine the amount $Q$ remaining after $t$ hours.

The half-life of a substance is 37 hours. If there are initially 145 grams of the substance, how many grams are remaining after 52 hours? Round your answer to 3 decimal places.

What is the doubling time of a population growing by $12 \%$ per year? Round your answer to the nearest hundredth of a year.

Quiz 5: Logarithmic Functions

Solve log⁡x=2\log x=2logx=2 for xxx .

Evaluate 10log⁡1310^{\log 13}10log13

Evaluate log⁡(1019)\log \left(10^{19}\right)log(1019)

Evaluate eln⁡9e^{\ln 9}eln9

Evaluate ln⁡(e9)\ln \left(e^{9}\right)ln(e9)

If the equation Q=8⋅31.7tQ=8 \cdot 3^{1.7 t}Q=8⋅31.7t is converted to the form Q=aektQ=a e^{k t}Q=aekt , then a=a=a= ----------- and k=k=k= ------------- Give k to 4 decimal places.

Let y=20e−0.07ty=20 e^{-0.07 t}y=20e−0.07t , with ttt measured in years. What is the continuous percent decay rate per year?

Let y=60e−0.07ty=60 e^{-0.07 t}y=60e−0.07t , with ttt measured in years. What is the percent annual decay rate? Round to 2 decimal places.

The doubling time for a bank account that is growing by 2.6%2.6 \%2.6% per year (compounded continually) is---------- years. Round 1 decimal place.

If Q=17e0.062tQ=\frac{1}{7} e^{0.062 t}Q=71​e0.062t is converted to the form Q=abtQ=a b^{t}Q=abt , then b=…b=\ldotsb=… . Round to 3 decimal places.

What is the half-life of a substance that decays at a rate of 3.21%3.21 \%3.21% per day? Round your answer to the nearest hundredth of a day.

What annual interest rate, compounded monthly, is equivalent to an annual interest rate of 5.4% compounded continuously? Round your answer to the nearest thousandth of a percent, if necessary.

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

Suppose the population of an endangered species is cut in half every 60 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 11%11 \%11% of a radioactive substance decays in 8 hours, what is the half-life of the substance in hours? Round your answer to 3 decimal places.

If 11%11 \%11% of a radioactive substance decays in 6 hours, what percent of the substance is left after 11 hours? Round your answer to 3 decimal places, if necessary.

The half-life of a substance is 34 hours. If there are initially 125 grams of the substance, write an exponential formula to determine the amount QQQ remaining after ttt hours.

The half-life of a substance is 37 hours. If there are initially 145 grams of the substance, how many grams are remaining after 52 hours? Round your answer to 3 decimal places.

What is the doubling time of a population growing by 12%12 \%12% per year? Round your answer to the nearest hundredth of a year.

Solve $\log x=2$ for $x$ .

Evaluate $10^{\log 13}$

Evaluate $\log \left(10^{19}\right)$

Evaluate $e^{\ln 9}$

Evaluate $\ln \left(e^{9}\right)$

If the equation $Q=8 \cdot 3^{1.7 t}$ is converted to the form $Q=a e^{k t}$ , then $a=$ ----------- and $k=$ ------------- Give k to 4 decimal places.

Let $y=20 e^{-0.07 t}$ , with $t$ measured in years. What is the continuous percent decay rate per year?

Let $y=60 e^{-0.07 t}$ , with $t$ measured in years. What is the percent annual decay rate? Round to 2 decimal places.

The doubling time for a bank account that is growing by $2.6 \%$ per year (compounded continually) is---------- years. Round 1 decimal place.

If $Q=\frac{1}{7} e^{0.062 t}$ is converted to the form $Q=a b^{t}$ , then $b=\ldots$ . Round to 3 decimal places.

What is the half-life of a substance that decays at a rate of $3.21 \%$ per day? Round your answer to the nearest hundredth of a day.

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?

If $11 \%$ of a radioactive substance decays in 8 hours, what is the half-life of the substance in hours? Round your answer to 3 decimal places.

If $11 \%$ of a radioactive substance decays in 6 hours, what percent of the substance is left after 11 hours? Round your answer to 3 decimal places, if necessary.

The half-life of a substance is 34 hours. If there are initially 125 grams of the substance, write an exponential formula to determine the amount $Q$ remaining after $t$ hours.

What is the doubling time of a population growing by $12 \%$ per year? Round your answer to the nearest hundredth of a year.