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

Level 1

This math topic focuses on solving for the initial quantity in various exponential growth scenarios using continuous rates. These problems cover applications such as social media views, bacteria population growth, company share prices, savings account interest accrual, and population increases, using specific percentages and time periods. Each problem involves rearranging an exponential growth formula to determine the starting value from a given future value, rate of growth, and time elapsed, further training on the practical application and understanding of exponential functions in real-world contexts.

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 Starting Value Worksheet

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Exponential Function Solution Equation - Growth (Continuous) Scenario...
1
A social media post starts with a certain number of views. Its view count grows continually by 7% each month.After 6 months it has 1,217 views.
Rearrange the exponential equation to solve for for the starting views given this scenario?
a A LaTex expression showing V sub 0 = 1217 over e to the power of (\frac{0.07 {6 )}}
b A LaTex expression showing V sub 0 = 1217 over e to the power of (0.07 times 6)
c A LaTex expression showing V sub 0 = \frac{e to the power of (0.07 times 6) }{1217}
2
A bacteria population starts at a certain size. It grows continuously at 5% growth per week. After 3 weeks it has increased to a population of 697.
Rearrange the exponential equation to solve for for the starting population given this scenario?
a A LaTex expression showing P sub 0 = 697 over e to the power of (\frac{0.05 {3 )}}
b A LaTex expression showing P sub 0 = 697 over e to the power of (0.05 times 3)
c A LaTex expression showing P sub 0 = \frac{e to the power of (0.05 times 3) }{697}
3
A company's share price starts at a certain value. It grows continuously at 4% growth per quarter. After 8 quarters it has a share price of $1,239.
Rearrange the exponential equation to solve for for the starting price given this scenario?
a A LaTex expression showing S sub 0 = 1239 over e to the power of (0.04 times 8)
b A LaTex expression showing S sub 0 = 1239 over e to the power of (\frac{0.04 {8 )}}
4
A bacteria population starts at a certain size. It grows continuously at 9% growth per month. After 8 months it has increased to a population of 410.
Rearrange the exponential equation to solve for for the starting population given this scenario?
a A LaTex expression showing P sub 0 = 410 over e to the power of (\frac{0.09 {8 )}}
b A LaTex expression showing P sub 0 = \frac{e to the power of (0.09 times 8) }{410}
c A LaTex expression showing P sub 0 = 410 over e to the power of (0.09 times 8)
5
A savings account starts with a certain amount of cash. It grows continuously at 2% interest per quarter. After 9 quarters it has $718.
Rearrange the exponential equation to solve for for the starting cash given this scenario?
a A LaTex expression showing P sub 0 = 718 over e to the power of (\frac{0.02 {9 )}}
b A LaTex expression showing P sub 0 = 718 over e to the power of (0.02 times 9)
c A LaTex expression showing P sub 0 = \frac{e to the power of (0.02 times 9) }{718}
6
A savings account starts with a certain amount of cash. It grows continuously at 3% interest per month. After 6 months it has $1,077.
Rearrange the exponential equation to solve for for the starting cash given this scenario?
a A LaTex expression showing P sub 0 = 1077 over e to the power of (\frac{0.03 {6 )}}
b A LaTex expression showing P sub 0 = \frac{e to the power of (0.03 times 6) }{1077}
c A LaTex expression showing P sub 0 = 1077 over e to the power of (0.03 times 6)
7
An insect population starts at a certain size. It grows continuously at 2% growth per year. After 4 years it has increased to a population of 866.
Rearrange the exponential equation to solve for for the starting population given this scenario?
a A LaTex expression showing P sub 0 = \frac{e to the power of (0.02 times 4) }{866}
b A LaTex expression showing P sub 0 = 866 over e to the power of (\frac{0.02 {4 )}}
c A LaTex expression showing P sub 0 = 866 over e to the power of (0.02 times 4)
8
A credit card starts with a certain amount of debt. It grows continuously at 4% interest per month. After 6 months the debt has grown to $635.
Rearrange the exponential equation to solve for for the starting debt given this scenario?
a A LaTex expression showing D sub 0 = 635 over e to the power of (0.04 times 6)
b A LaTex expression showing D sub 0 = \frac{e to the power of (0.04 times 6) }{635}
c A LaTex expression showing D sub 0 = 635 over e to the power of (\frac{0.04 {6 )}}