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

Level 1

This math topic involves solving for the initial values in various scenarios modeled by exponential growth with continuous compounding. Specifically, it covers solving exponential equations related to growth models in a range of real-world contexts such as app downloads, share prices, savings account balances, business and social media metrics, and biological populations. Each problem provides an exponential growth equation, and students are asked to derive the starting quantity (like initial amount of money, initial population, or initial price) from the given formula.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Exponential Function Solving - Growth (Continuous) Equation to Starting Value Worksheet

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Exponential Function Solving - Growth (Continuous) Equation to Starti...
1
Solve for the starting downloads given this model of a continuously compounding growth of app downloads?
A LaTex expression showing 1,045 =A sub 0 times e to the power of (0.03 times 5)
a A LaTex expression showing 0 + A sub 0 = A over e to the power of (\frac{r {t )}}
b A LaTex expression showing 4 + A sub 0 = \frac{e to the power of (r times t) }{A}
c A LaTex expression showing 1 + A sub 0 = \frac{e to the power of (r times t) }{A}
d A LaTex expression showing A sub 0 = A over e to the power of (r times t)
2
Solve for the starting price given this model of a continuously compounding growth of a share price?
A LaTex expression showing 901 =S sub 0 times e to the power of (0.02 times 6)
a A LaTex expression showing 8 + S sub 0 = S over e to the power of (\frac{r {t )}}
b A LaTex expression showing S sub 0 = S over e to the power of (r times t)
c A LaTex expression showing 6 + S sub 0 = S over e to the power of (\frac{r {t )}}
d A LaTex expression showing 0 + S sub 0 = S over e to the power of (\frac{r {t )}}
3
Solve for the starting cash given this model of a continuously compounding growth of money in a savings account?
A LaTex expression showing 760 =P sub 0 times e to the power of (0.07 times 6)
a A LaTex expression showing 4 + P sub 0 = P over e to the power of (\frac{r {t )}}
b A LaTex expression showing 6 + P sub 0 = P over e to the power of (\frac{r {t )}}
c A LaTex expression showing P sub 0 = P over e to the power of (r times t)
4
Solve for the starting population given this model of a continuous growth of a rabbit population?
A LaTex expression showing 345 =P sub 0 times e to the power of (0.02 times 7)
a A LaTex expression showing 0 + P sub 0 = P over e to the power of (\frac{r {t )}}
b A LaTex expression showing 5 + P sub 0 = \frac{e to the power of (r times t) }{P}
c A LaTex expression showing 2 + P sub 0 = \frac{e to the power of (r times t) }{P}
d A LaTex expression showing P sub 0 = P over e to the power of (r times t)
5
Solve for the starting debt given this model of a growth of debt on a credit card with continuous compounding?
A LaTex expression showing 635 =D sub 0 times e to the power of (0.06 times 4)
a A LaTex expression showing 0 + D sub 0 = \frac{e to the power of (r times t) }{D}
b A LaTex expression showing 7 + D sub 0 = D over e to the power of (\frac{r {t )}}
c A LaTex expression showing D sub 0 = D over e to the power of (r times t)
d A LaTex expression showing 3 + D sub 0 = D over e to the power of (\frac{r {t )}}
6
Solve for the starting population given this model of a continuous growth of an insect population?
A LaTex expression showing 1,214 =P sub 0 times e to the power of (0.05 times 6)
a A LaTex expression showing 5 + P sub 0 = P over e to the power of (\frac{r {t )}}
b A LaTex expression showing P sub 0 = P over e to the power of (r times t)
c A LaTex expression showing 3 + P sub 0 = \frac{e to the power of (r times t) }{P}
d A LaTex expression showing 9 + P sub 0 = \frac{e to the power of (r times t) }{P}
7
Solve for the starting views given this model of a continuous exponential growth of social media post views?
A LaTex expression showing 396 =V sub 0 times e to the power of (0.07 times 4)
a A LaTex expression showing 1 + V sub 0 = V over e to the power of (\frac{r {t )}}
b A LaTex expression showing 1 + V sub 0 = \frac{e to the power of (r times t) }{V}
c A LaTex expression showing V sub 0 = V over e to the power of (r times t)
d A LaTex expression showing 2 + V sub 0 = V over e to the power of (\frac{r {t )}}
8
Solve for the starting downloads given this model of a continuously compounding growth of app downloads?
A LaTex expression showing 700 =A sub 0 times e to the power of (0.07 times 8)
a A LaTex expression showing 3 + A sub 0 = \frac{e to the power of (r times t) }{A}
b A LaTex expression showing 4 + A sub 0 = \frac{e to the power of (r times t) }{A}
c A LaTex expression showing A sub 0 = A over e to the power of (r times t)
d A LaTex expression showing 7 + A sub 0 = \frac{e to the power of (r times t) }{A}