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

Level 1

This math topic focuses on solving for the rate of growth using exponential functions in continuous growth scenarios. It covers practical application of exponential functions in various contexts such as population growth of insects and rabbits, compound interest growth in savings accounts, and social media post views. The problems involve rearranging exponential equations to isolate and calculate the growth rate (r) using both natural log (ln) and exponential 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) Equation to Rate Worksheet

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Exponential Function Solution Equation - Growth (Continuous) Equation...
1
A LaTex expression showing 938 =500 times e to the power of (r times 9)
Rearrange this equation to solve for the rate given this model of a continuous growth of an insect population?
a A LaTex expression showing r = +\ln{\frac{938 over 500 }}{9}
b A LaTex expression showing r = +e to the power of \frac{938 over 500 }{9}
2
Rearrange this equation to solve for the rate given this model of a continuous growth of a rabbit population?
A LaTex expression showing 1,232 =600 times e to the power of (r times 9)
a A LaTex expression showing r = +\ln{\frac{1232 over 600 }}{9}
b A LaTex expression showing r = +\ln{\frac{600 over 1232 }}{9}
3
Rearrange this equation to solve for the rate given this model of a continuous growth of a rabbit population?
A LaTex expression showing 1,079 =800 times e to the power of (r times 6)
a A LaTex expression showing r = +e to the power of \frac{1079 over 800 }{6}
b A LaTex expression showing r = +\ln{\frac{1079 over 800 }}{6}
4
Rearrange this equation to solve for the rate given this model of a continuously compounding growth of money in a savings account?
A LaTex expression showing 425 =300 times e to the power of (r times 7)
a A LaTex expression showing r = +e to the power of \frac{425 over 300 }{7}
b A LaTex expression showing r = +\ln{\frac{425 over 300 }}{7}
c A LaTex expression showing r = +\ln{\frac{300 over 425 }}{7}
5
Rearrange this equation to solve for the rate given this model of a continuously compounding growth of money in a savings account?
A LaTex expression showing 1,131 =700 times e to the power of (r times 6)
a A LaTex expression showing r = +e to the power of \frac{1131 over 700 }{6}
b A LaTex expression showing r = +\ln{\frac{700 over 1131 }}{6}
c A LaTex expression showing r = +\ln{\frac{1131 over 700 }}{6}
6
Rearrange this equation to solve for the rate given this model of a continuous growth of an insect population?
A LaTex expression showing 1,110 =900 times e to the power of (r times 7)
a A LaTex expression showing r = +\ln{\frac{1110 over 900 }}{7}
b A LaTex expression showing r = +e to the power of \frac{1110 over 900 }{7}
7
A LaTex expression showing 396 =300 times e to the power of (r times 4)
Rearrange this equation to solve for the rate given this model of a continuous exponential growth of social media post views?
a A LaTex expression showing r = +\ln{\frac{396 over 300 }}{4}
b A LaTex expression showing r = +e to the power of \frac{396 over 300 }{4}
8
Rearrange this equation to solve for the rate given this model of a continuous growth of an insect population?
A LaTex expression showing 567 =400 times e to the power of (r times 7)
a A LaTex expression showing r = +\ln{\frac{567 over 400 }}{7}
b A LaTex expression showing r = +e to the power of \frac{567 over 400 }{7}
c A LaTex expression showing r = +\ln{\frac{400 over 567 }}{7}