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

Level 1

This math topic focuses on solving for the starting value in continuous growth scenarios using exponential functions. The problems involve different contexts such as financial debt, population growth of bacteria, social media metrics, and wildlife studies. The skills practiced include understanding the properties of exponential growth, applying the formula for continuous growth (using natural exponential functions), and rearranging the formula to solve for the initial quantity before growth. The problems provide real-life scenarios where growth rates and final amounts are given and require calculating the original amount before the growth began.

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

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

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Exponential Function Solving - Growth (Continuous) Scenario to Starti...
1
A credit card starts with a certain amount of debt. It grows continuously at 5% interest per month. After 3 months the debt has grown to $1,045.
Solve for the starting debt given this scenario?
a A LaTex expression showing 5 + D sub 0 = \frac{e to the power of (r times t) }{D}
b A LaTex expression showing D sub 0 = D over e to the power of (r times t)
c A LaTex expression showing 8 + D sub 0 = D over e to the power of (\frac{r {t )}}
d A LaTex expression showing 5 + D sub 0 = D over e to the power of (\frac{r {t )}}
2
A bacteria population starts at a certain size. It grows continuously at 3% growth per year. After 5 years it has increased to a population of 929.
Solve for the starting population given this scenario?
a A LaTex expression showing 3 + 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 8 + P sub 0 = P over e to the power of (\frac{r {t )}}
d A LaTex expression showing P sub 0 = P over e to the power of (r times t)
3
A social media post starts with a certain number of views. Its view count grows continually by 8% each week.After 6 weeks it has 646 views.
Solve for the starting views given this scenario?
a A LaTex expression showing 7 + V sub 0 = V over e to the power of (\frac{r {t )}}
b A LaTex expression showing 1 + V sub 0 = V over e to the power of (\frac{r {t )}}
c A LaTex expression showing V sub 0 = V over e to the power of (r times t)
d A LaTex expression showing 0 + V sub 0 = V over e to the power of (\frac{r {t )}}
4
An insect population starts at a certain size. It grows continuously at 7% growth per year. After 6 years it has increased to a population of 456.
Solve for the starting population given this scenario?
a A LaTex expression showing 6 + P sub 0 = \frac{e to the power of (r times t) }{P}
b A LaTex expression showing P sub 0 = P over e to the power of (r times t)
c A LaTex expression showing 4 + P sub 0 = \frac{e to the power of (r times t) }{P}
5
An insect population starts at a certain size. It grows continuously at 4% growth per year. After 8 years it has increased to a population of 688.
Solve for the starting population given this scenario?
a A LaTex expression showing 8 + P sub 0 = \frac{e to the power of (r times t) }{P}
b A LaTex expression showing P sub 0 = P over e to the power of (r times t)
c A LaTex expression showing 2 + P sub 0 = \frac{e to the power of (r times t) }{P}
d A LaTex expression showing 0 + P sub 0 = \frac{e to the power of (r times t) }{P}
6
A bacteria population starts at a certain size. It grows continuously at 6% growth per week. After 2 weeks it has increased to a population of 901.
Solve for the starting population given this scenario?
a A LaTex expression showing P sub 0 = P over e to the power of (r times t)
b A LaTex expression showing 9 + P sub 0 = \frac{e to the power of (r times t) }{P}
c A LaTex expression showing 0 + P sub 0 = P over e to the power of (\frac{r {t )}}
d A LaTex expression showing 2 + P sub 0 = \frac{e to the power of (r times t) }{P}
7
A bacteria population starts at a certain size. It grows continuously at 8% growth per year. After 6 years it has increased to a population of 1,454.
Solve for the starting population given this scenario?
a A LaTex expression showing 4 + P sub 0 = \frac{e to the power of (r times t) }{P}
b A LaTex expression showing 3 + 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)
d A LaTex expression showing 9 + P sub 0 = P over e to the power of (\frac{r {t )}}
8
An insect population starts at a certain size. It grows continuously at 6% growth per day. After 9 days it has increased to a population of 514.
Solve for the starting population given this scenario?
a A LaTex expression showing P sub 0 = P over e to the power of (r times t)
b A LaTex expression showing 0 + P sub 0 = \frac{e to the power of (r times t) }{P}
c A LaTex expression showing 3 + P sub 0 = P over e to the power of (\frac{r {t )}}
d A LaTex expression showing 7 + P sub 0 = \frac{e to the power of (r times t) }{P}