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Exponential Function Solving - Growth (Continuous, Mis-matched Time Units) Scenario to Starting Value

Level 1

The topics in this unit focus on mastering exponential growth and decay functions. Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Exponential Function Solving - Growth (Continuous, Mis-matched Time Units) Scenario to Starting Value Worksheet

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Exponential Function Solving - Growth (Continuous, Mis-matched Time U...
1
An app starts with a certain number of downloads. Its download count grows continually by 9% each day.After 3 weeks it has 916 downloads.
How would you solve for the starting downloads given this scenario?
a A LaTex expression showing A sub 0 = A over e to the power of (\frac{r {t over 7 )}}
b A LaTex expression showing A sub 0 = A over e to the power of (r times t times 7)
2
A rabbit population starts at a certain size. It grows continuously at 8% growth per year. After 9 quarters it has increased to a population of 1,438 rabbits.
How would you solve for the starting population given this scenario?
a A LaTex expression showing P sub 0 = e to the power of (r times \frac{t over 4 ) }{P}
b A LaTex expression showing P sub 0 = P over e to the power of (\frac{r {t times 4 )}}
c A LaTex expression showing P sub 0 = P over e to the power of (r times \frac{t {4 )}}
3
An app starts with a certain number of downloads. Its download count grows continually by 9% each year.After 5 months it has 940 downloads.
How would you solve for the starting downloads given this scenario?
a A LaTex expression showing A sub 0 = A over e to the power of (r times \frac{t {12 )}}
b A LaTex expression showing A sub 0 = e to the power of (r times \frac{t over 12 ) }{A}
c A LaTex expression showing A sub 0 = A over e to the power of (\frac{r {t times 12 )}}
4
A bacteria population starts at a certain size. It grows continuously at 7% growth per year. After 2 days it has increased to a population of 460.
How would you solve for the starting population given this scenario?
a A LaTex expression showing P sub 0 = P over e to the power of (\frac{r {t times 365 )}}
b A LaTex expression showing P sub 0 = e to the power of (r times \frac{t over 365 ) }{P}
c A LaTex expression showing P sub 0 = P over e to the power of (r times \frac{t {365 )}}
5
A savings account starts with a certain amount of cash. It grows continuously at 3% interest per year. After 7 months it has $1,110.
How would you solve for the starting cash given this scenario?
a A LaTex expression showing P sub 0 = P over e to the power of (\frac{r {t times 12 )}}
b A LaTex expression showing P sub 0 = P over e to the power of (r times \frac{t {12 )}}
6
A social media post starts with a certain number of views. Its view count grows continually by 5% each week.After 4 days it has 366 views.
How would you solve for the starting views given this scenario?
a A LaTex expression showing V sub 0 = e to the power of (r times \frac{t over 7 ) }{V}
b A LaTex expression showing V sub 0 = V over e to the power of (r times \frac{t {7 )}}
7
An insect population starts at a certain size. It grows continuously at 8% growth per day. After 2 weeks it has increased to a population of 469.
How would you solve for the starting population given this scenario?
a A LaTex expression showing P sub 0 = \frac{e to the power of (r times t times 7) }{P}
b A LaTex expression showing P sub 0 = P over e to the power of (r times t times 7)
8
A credit card starts with a certain amount of debt. It grows continuously at 8% interest per year. After 6 months the debt has grown to $1,454.
How would you solve for the starting debt given this scenario?
a A LaTex expression showing D sub 0 = e to the power of (r times \frac{t over 12 ) }{D}
b A LaTex expression showing D sub 0 = D over e to the power of (\frac{r {t times 12 )}}
c A LaTex expression showing D sub 0 = D over e to the power of (r times \frac{t {12 )}}