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Exponential Function Solution Equation - Growth (Continuous, Mis-matched Time Units) - Scenario to Time

Level 1

The topics in this unit focus on mastering exponential growth and decay functions. 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, Mis-matched Time Units) - Scenario to Time Worksheet

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Exponential Function Solution Equation - Growth (Continuous, Mis-matc...
1
A credit card starts with $500 of debt. It grows continuously at 9% interest per year. After a certain number of months the debt has grown to $598.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = 12 times \ln{\frac{598 over 500 }}{0.09}
b A LaTex expression showing t = -1 over 12 times \frac{\ln{598 times 500}}{0.09}
c A LaTex expression showing t = 12 times 0.09 over \ln{\frac{598 {500}}}
2
A credit card starts with $900 of debt. It grows continuously at 8% interest per month. After a certain number of quarters the debt has grown to $1,575.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = -3 times \frac{\ln{1575 times 900}}{0.08}
b A LaTex expression showing t = 1 over 3 times \ln{\frac{1575 over 900 }}{0.08}
3
An insect population starts at 400. It grows continuously at 7% growth per month. After a certain number of years it has increased to a population of 751.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = 1 over 12 times \ln{\frac{751 over 400 }}{0.07}
b A LaTex expression showing t = 12 times \ln{\frac{751 over 400 }}{0.07}
c A LaTex expression showing t = -12 times \frac{\ln{751 times 400}}{0.07}
4
A bacteria population starts at 600. It grows continuously at 7% growth per day. After a certain number of years it has increased to a population of 1,126.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = 1 over 365 times 0.07 over \ln{\frac{1126 {600}}}
b A LaTex expression showing t = 1 over 365 times \ln{\frac{1126 over 600 }}{0.07}
c A LaTex expression showing t = 365 times \ln{\frac{1126 over 600 }}{0.07}
5
An insect population starts at 200. It grows continuously at 8% growth per week. After a certain number of days it has increased to a population of 323.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = 7 times \ln{\frac{323 over 200 }}{0.08}
b A LaTex expression showing t = 1 over 7 times \ln{\frac{323 over 200 }}{0.08}
c A LaTex expression showing t = 7 times 0.08 over \ln{\frac{323 {200}}}
6
A rabbit population starts at 600. It grows continuously at 4% growth per quarter. After a certain number of years it has increased to a population of 649 rabbits.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = -4 times \frac{\ln{649 times 600}}{0.04}
b A LaTex expression showing t = 4 times \ln{\frac{649 over 600 }}{0.04}
c A LaTex expression showing t = 1 over 4 times \ln{\frac{649 over 600 }}{0.04}
7
A credit card starts with $600 of debt. It grows continuously at 7% interest per month. After a certain number of quarters the debt has grown to $851.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = 3 times \ln{\frac{851 over 600 }}{0.07}
b A LaTex expression showing t = 1 over 3 times \ln{\frac{851 over 600 }}{0.07}
c A LaTex expression showing t = -3 times \frac{\ln{851 times 600}}{0.07}
8
A credit card starts with $300 of debt. It grows continuously at 2% interest per year. After a certain number of quarters the debt has grown to $345.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = 4 times \ln{\frac{345 over 300 }}{0.02}
b A LaTex expression showing t = 1 over 4 times \ln{\frac{345 over 300 }}{0.02}
c A LaTex expression showing t = 4 times 0.02 over \ln{\frac{345 {300}}}
d A LaTex expression showing t = -1 over 4 times \frac{\ln{345 times 300}}{0.02}