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Exponential Function Solution Equation - Growth (Continuous) - Scenario to Time

Level 1

This math topic involves solving problems related to continuous exponential growth, specifically focusing on rearranging exponential equations to find time durations in various scenarios. There are problems involving financial topics like credit card debt and shares, biological growth like bacteria populations, and general increase such as app downloads and savings accounts. Each problem provides a growth rate and final value to aid in solving using logarithmic equations to determine the time required to reach that value from a specified initial value.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Exponential Function Solution Equation - Growth (Continuous) - Scenario to Time Worksheet

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Exponential Function Solution Equation - Growth (Continuous) - Scenar...
1
A company's share price starts at $300. It grows continuously at 5% growth per quarter. After a certain number of quarters it has a share price of $331.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = -\frac{\ln{331 times 300}}{0.05}
b A LaTex expression showing t = +\ln{\frac{331 over 300 }}{0.05}
c A LaTex expression showing t = +0.05 over \ln{\frac{331 {300}}}
2
A bacteria population starts at 500. It grows continuously at 7% growth per day. After a certain number of days it has increased to a population of 575.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = +\ln{\frac{575 over 500 }}{0.07}
b A LaTex expression showing t = -\frac{\ln{575 times 500}}{0.07}
c A LaTex expression showing t = +0.07 over \ln{\frac{575 {500}}}
3
A credit card starts with $300 of debt. It grows continuously at 5% interest per year. After a certain number of years the debt has grown to $366.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = -\frac{\ln{366 times 300}}{0.05}
b A LaTex expression showing t = +0.05 over \ln{\frac{366 {300}}}
c A LaTex expression showing t = +\ln{\frac{366 over 300 }}{0.05}
4
A credit card starts with $800 of debt. It grows continuously at 6% interest per quarter. After a certain number of quarters the debt has grown to $1,079.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = +\ln{\frac{1079 over 800 }}{0.06}
b A LaTex expression showing t = +0.06 over \ln{\frac{1079 {800}}}
c A LaTex expression showing t = -\frac{\ln{1079 times 800}}{0.06}
5
A savings account starts with $400. It grows continuously at 7% interest per month. After a certain number of months it has $700.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = -\frac{\ln{700 times 400}}{0.07}
b A LaTex expression showing t = +0.07 over \ln{\frac{700 {400}}}
c A LaTex expression showing t = +\ln{\frac{700 over 400 }}{0.07}
6
An app starts with 200 downloads. Its download count grows continually by 6% each year.After a certain number of years it has 323 downloads.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = -\frac{\ln{323 times 200}}{0.06}
b A LaTex expression showing t = +0.06 over \ln{\frac{323 {200}}}
c A LaTex expression showing t = +\ln{\frac{323 over 200 }}{0.06}
7
A credit card starts with $500 of debt. It grows continuously at 8% interest per year. After a certain number of years the debt has grown to $875.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = +0.08 over \ln{\frac{875 {500}}}
b A LaTex expression showing t = +\ln{\frac{875 over 500 }}{0.08}
c A LaTex expression showing t = -\frac{\ln{875 times 500}}{0.08}
8
A savings account starts with $500. It grows continuously at 2% interest per year. After a certain number of years it has $541.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = +\ln{\frac{541 over 500 }}{0.02}
b A LaTex expression showing t = -\frac{\ln{541 times 500}}{0.02}