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Exponential Function Solving - 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 Solving - Growth (Continuous, Mis-matched Time Units) Scenario to Rate Worksheet

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Exponential Function Solving - Growth (Continuous, Mis-matched Time U...
1
An insect population starts at 500. It grows continuously at a certain percent growth per year. After 4 days it has increased to a population of 688.
How would you solve for the rate given this scenario?
a A LaTex expression showing r = +e to the power of \frac{P over P sub 0 }{t over 365 }
b A LaTex expression showing r = +\ln{\frac{P over P sub 0 }}{t over 365 }
2
A savings account starts with $500. It grows continuously at a certain percent interest per quarter. After 9 months it has $716.
How would you solve for the rate given this scenario?
a A LaTex expression showing r = +e to the power of \frac{P over P sub 0 }{t over 3 }
b A LaTex expression showing r = +\ln{\frac{P over P sub 0 }}{t over 3 }
3
An insect population starts at 400. It grows continuously at a certain percent growth per week. After 7 days it has increased to a population of 608.
How would you solve for the rate given this scenario?
a A LaTex expression showing r = +\ln{\frac{P over P sub 0 }}{t over 7 }
b A LaTex expression showing r = +e to the power of \frac{P over P sub 0 }{t over 7 }
c A LaTex expression showing r = +\ln{\frac{P sub 0 over P }}{t times 7}
4
A rabbit population starts at 700. It grows continuously at a certain percent growth per year. After 2 quarters it has increased to a population of 758 rabbits.
How would you solve for the rate given this scenario?
a A LaTex expression showing r = +\ln{\frac{P over P sub 0 }}{t over 4 }
b A LaTex expression showing r = +\ln{\frac{P sub 0 over P }}{t times 4}
c A LaTex expression showing r = +e to the power of \frac{P over P sub 0 }{t over 4 }
5
An app starts with 800 downloads. Its download count grows continually by a certain percent each week. After 7 days it has 1,135 downloads.
How would you solve for the rate given this scenario?
a A LaTex expression showing r = +\ln{\frac{A over A sub 0 }}{t over 7 }
b A LaTex expression showing r = +e to the power of \frac{A over A sub 0 }{t over 7 }
c A LaTex expression showing r = +\ln{\frac{A sub 0 over A }}{t times 7}
6
A savings account starts with $900. It grows continuously at a certain percent interest per year. After 4 months it has $974.
How would you solve for the rate given this scenario?
a A LaTex expression showing r = +e to the power of \frac{P over P sub 0 }{t over 12 }
b A LaTex expression showing r = +\ln{\frac{P over P sub 0 }}{t over 12 }
c A LaTex expression showing r = +\ln{\frac{P sub 0 over P }}{t times 12}
7
A savings account starts with $400. It grows continuously at a certain percent interest per year. After 9 months it has $478.
How would you solve for the rate given this scenario?
a A LaTex expression showing r = +\ln{\frac{P over P sub 0 }}{t over 12 }
b A LaTex expression showing r = +e to the power of \frac{P over P sub 0 }{t over 12 }
c A LaTex expression showing r = +\ln{\frac{P sub 0 over P }}{t times 12}
8
A company's share price starts at $200. It grows continuously at a certain percent growth per quarter. After 8 months it has a share price of $254.
How would you solve for the rate given this scenario?
a A LaTex expression showing r = +\ln{\frac{S over S sub 0 }}{t over 3 }
b A LaTex expression showing r = +e to the power of \frac{S over S sub 0 }{t over 3 }
c A LaTex expression showing r = +\ln{\frac{S sub 0 over S }}{t times 3}