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Exponential Function Solution Equation - Growth (Continuous) Equation to Starting Value

Level 1

This math topic focuses on rearranging exponential growth equations to solve for initial values in various scenarios, such as social media views, credit card debt, application downloads, and animal populations. It teaches how to manipulate the formulas of continuously compounding growth to isolate and compute starting values given the final count after a certain period at a specified growth rate. The students need to understand the properties of exponential functions and logarithms to solve these problems.

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 Starting Value Worksheet

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Exponential Function Solution Equation - Growth (Continuous) Equation...
1
Rearrange this equation to solve for the starting views given this model of a continuous exponential growth of social media post views?
A LaTex expression showing 1,438 =V sub 0 times e to the power of (0.08 times 9)
a A LaTex expression showing V sub 0 = 1438 over e to the power of (0.08 times 9)
b A LaTex expression showing V sub 0 = \frac{e to the power of (0.08 times 9) }{1438}
c A LaTex expression showing V sub 0 = 1438 over e to the power of (\frac{0.08 {9 )}}
2
Rearrange this equation to solve for the starting debt given this model of a growth of debt on a credit card with continuous compounding?
A LaTex expression showing 854 =D sub 0 times e to the power of (0.05 times 4)
a A LaTex expression showing D sub 0 = 854 over e to the power of (\frac{0.05 {4 )}}
b A LaTex expression showing D sub 0 = 854 over e to the power of (0.05 times 4)
c A LaTex expression showing D sub 0 = \frac{e to the power of (0.05 times 4) }{854}
3
Rearrange this equation to solve for the starting downloads given this model of a continuously compounding growth of app downloads?
A LaTex expression showing 1,232 =A sub 0 times e to the power of (0.09 times 8)
a A LaTex expression showing A sub 0 = 1232 over e to the power of (0.09 times 8)
b A LaTex expression showing A sub 0 = \frac{e to the power of (0.09 times 8) }{1232}
c A LaTex expression showing A sub 0 = 1232 over e to the power of (\frac{0.09 {8 )}}
4
Rearrange this equation to solve for the starting downloads given this model of a continuously compounding growth of app downloads?
A LaTex expression showing 530 =A sub 0 times e to the power of (0.03 times 2)
a A LaTex expression showing A sub 0 = 530 over e to the power of (\frac{0.03 {2 )}}
b A LaTex expression showing A sub 0 = \frac{e to the power of (0.03 times 2) }{530}
c A LaTex expression showing A sub 0 = 530 over e to the power of (0.03 times 2)
5
Rearrange this equation to solve for the starting population given this model of a continuous growth of a rabbit population?
A LaTex expression showing 676 =P sub 0 times e to the power of (0.04 times 3)
a A LaTex expression showing P sub 0 = \frac{e to the power of (0.04 times 3) }{676}
b A LaTex expression showing P sub 0 = 676 over e to the power of (0.04 times 3)
c A LaTex expression showing P sub 0 = 676 over e to the power of (\frac{0.04 {3 )}}
6
Rearrange this equation to solve for the starting debt given this model of a growth of debt on a credit card with continuous compounding?
A LaTex expression showing 442 =D sub 0 times e to the power of (0.02 times 5)
a A LaTex expression showing D sub 0 = 442 over e to the power of (0.02 times 5)
b A LaTex expression showing D sub 0 = \frac{e to the power of (0.02 times 5) }{442}
c A LaTex expression showing D sub 0 = 442 over e to the power of (\frac{0.02 {5 )}}
7
Rearrange this equation to solve for the starting downloads given this model of a continuously compounding growth of app downloads?
A LaTex expression showing 627 =A sub 0 times e to the power of (0.09 times 5)
a A LaTex expression showing A sub 0 = 627 over e to the power of (0.09 times 5)
b A LaTex expression showing A sub 0 = \frac{e to the power of (0.09 times 5) }{627}
c A LaTex expression showing A sub 0 = 627 over e to the power of (\frac{0.09 {5 )}}
8
Rearrange this equation to solve for the starting debt given this model of a growth of debt on a credit card with continuous compounding?
A LaTex expression showing 352 =D sub 0 times e to the power of (0.08 times 2)
a A LaTex expression showing D sub 0 = 352 over e to the power of (0.08 times 2)
b A LaTex expression showing D sub 0 = \frac{e to the power of (0.08 times 2) }{352}
c A LaTex expression showing D sub 0 = 352 over e to the power of (\frac{0.08 {2 )}}