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

Level 1

This math topic focuses on skills related to understanding and manipulating exponential growth equations in continuous growth scenarios. Problems involve situations such as continuously growing company share prices, savings account balances, and credit card debts. The tasks required include rearranging exponential functions to solve for the continuous growth rate, given the initial and final amounts, and the time elapsed. The aim is to determine the formula expressing the growth rate in terms of logarithmic (Ln) or exponential (e) functions. Each exercise is provided with several potential answers in the form of mathematical expressions.

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 Rate Worksheet

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Exponential Function Solution Equation - Growth (Continuous) Scenario...
1
A company's share price starts at $500. It grows continuously at a certain percent growth per quarter. After 6 quarters it has a share price of $808.
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{808 over 500 }{6}
b A LaTex expression showing r = +\ln{\frac{808 over 500 }}{6}
2
A savings account starts with $500. It grows continuously at a certain percent interest per month. After 2 months it has $586.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = +\ln{\frac{500 over 586 }}{2}
b A LaTex expression showing r = +e to the power of \frac{586 over 500 }{2}
c A LaTex expression showing r = +\ln{\frac{586 over 500 }}{2}
3
A credit card starts with $300 of debt. It grows continuously at a certain percent interest per year. After 6 years the debt has grown to $404.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = +\ln{\frac{300 over 404 }}{6}
b A LaTex expression showing r = +\ln{\frac{404 over 300 }}{6}
c A LaTex expression showing r = +e to the power of \frac{404 over 300 }{6}
4
A company's share price starts at $500. It grows continuously at a certain percent growth per month. After 9 months it has a share price of $938.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = +\ln{\frac{500 over 938 }}{9}
b A LaTex expression showing r = +\ln{\frac{938 over 500 }}{9}
c A LaTex expression showing r = +e to the power of \frac{938 over 500 }{9}
5
A credit card starts with $200 of debt. It grows continuously at a certain percent interest per month. After 6 months the debt has grown to $323.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = +\ln{\frac{323 over 200 }}{6}
b A LaTex expression showing r = +e to the power of \frac{323 over 200 }{6}
c A LaTex expression showing r = +\ln{\frac{200 over 323 }}{6}
6
A company's share price starts at $900. It grows continuously at a certain percent growth per quarter. After 2 quarters it has a share price of $1,035.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = +\ln{\frac{1035 over 900 }}{2}
b A LaTex expression showing r = +e to the power of \frac{1035 over 900 }{2}
c A LaTex expression showing r = +\ln{\frac{900 over 1035 }}{2}
7
A company's share price starts at $200. It grows continuously at a certain percent growth per year. After 4 years it has a share price of $225.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = +\ln{\frac{225 over 200 }}{4}
b A LaTex expression showing r = +\ln{\frac{200 over 225 }}{4}
c A LaTex expression showing r = +e to the power of \frac{225 over 200 }{4}
8
A bacteria population starts at 200. It grows continuously at a certain percent growth per year. After 9 years it has increased to a population of 261.
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{261 over 200 }{9}
b A LaTex expression showing r = +\ln{\frac{200 over 261 }}{9}
c A LaTex expression showing r = +\ln{\frac{261 over 200 }}{9}