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

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 Rate Worksheet

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Exponential Function Solution Equation - Growth (Continuous, Mis-matc...
1
A company's share price starts at $400. It grows continuously at a certain percent growth per year. After 2 months it has a share price of $469.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = \ln{\frac{469 over 400 }}{2 over 12 }
b A LaTex expression showing r = e to the power of \frac{469 over 400 }{2 over 12 }
2
An app starts with 800 downloads. Its download count grows continually by a certain percent each day. After 4 years it has 1,146 downloads.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = \ln{\frac{1146 over 800 }}{4 times 365}
b A LaTex expression showing r = e to the power of \frac{1146 over 800 }{4 times 365}
c A LaTex expression showing r = \ln{\frac{800 over 1146 }}{4 over 365 }
3
A credit card starts with $600 of debt. It grows continuously at a certain percent interest per quarter. After 5 months the debt has grown to $732.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = \ln{\frac{732 over 600 }}{5 over 3 }
b A LaTex expression showing r = e to the power of \frac{732 over 600 }{5 over 3 }
4
A bacteria population starts at 200. It grows continuously at a certain percent growth per year. After 5 days it has increased to a population of 283.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = \ln{\frac{200 over 283 }}{5 times 365}
b A LaTex expression showing r = \ln{\frac{283 over 200 }}{5 over 365 }
c A LaTex expression showing r = e to the power of \frac{283 over 200 }{5 over 365 }
5
A bacteria population starts at 600. It grows continuously at a certain percent growth per year. After 7 days it has increased to a population of 740.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = \ln{\frac{600 over 740 }}{7 times 365}
b A LaTex expression showing r = \ln{\frac{740 over 600 }}{7 over 365 }
c A LaTex expression showing r = e to the power of \frac{740 over 600 }{7 over 365 }
6
A credit card starts with $800 of debt. It grows continuously at a certain percent interest per quarter. After 4 months the debt has grown to $1,146.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = \ln{\frac{800 over 1146 }}{4 times 3}
b A LaTex expression showing r = e to the power of \frac{1146 over 800 }{4 over 3 }
c A LaTex expression showing r = \ln{\frac{1146 over 800 }}{4 over 3 }
7
A savings account starts with $300. It grows continuously at a certain percent interest per quarter. After 5 months it has $447.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = \ln{\frac{300 over 447 }}{5 times 3}
b A LaTex expression showing r = \ln{\frac{447 over 300 }}{5 over 3 }
c A LaTex expression showing r = e to the power of \frac{447 over 300 }{5 over 3 }
8
A company's share price starts at $400. It grows continuously at a certain percent growth per month. After 2 years it has a share price of $424.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = e to the power of \frac{424 over 400 }{2 times 12}
b A LaTex expression showing r = \ln{\frac{424 over 400 }}{2 times 12}
c A LaTex expression showing r = \ln{\frac{400 over 424 }}{2 over 12 }