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

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Exponential Function Solution Equation - Growth (Continuous, Mis-matc...
1
A bacteria population starts at a certain size. It grows continuously at 3% growth per day. After 7 years it has increased to a population of 493.
Rearrange the exponential equation to solve for for the starting population given this scenario?
a A LaTex expression showing P sub 0 = 493 over e to the power of (0.03 times 7 times 365)
b A LaTex expression showing P sub 0 = \frac{e to the power of (0.03 times 7 times 365) }{493}
c A LaTex expression showing P sub 0 = 493 over e to the power of (\frac{0.03 {7 over 365 )}}
2
A rabbit population starts at a certain size. It grows continuously at 4% growth per year. After 6 quarters it has increased to a population of 635 rabbits.
Rearrange the exponential equation to solve for for the starting population given this scenario?
a A LaTex expression showing P sub 0 = 635 over e to the power of (\frac{0.04 {6 times 4 )}}
b A LaTex expression showing P sub 0 = 635 over e to the power of (0.04 times \frac{6 {4 )}}
3
A social media post starts with a certain number of views. Its view count grows continually by 2% each day.After 6 years it has 563 views.
Rearrange the exponential equation to solve for for the starting views given this scenario?
a A LaTex expression showing V sub 0 = 563 over e to the power of (0.02 times 6 times 365)
b A LaTex expression showing V sub 0 = 563 over e to the power of (\frac{0.02 {6 over 365 )}}
4
A company's share price starts at a certain value. It grows continuously at 9% growth per quarter. After 3 years it has a share price of $1,047.
Rearrange the exponential equation to solve for for the starting price given this scenario?
a A LaTex expression showing S sub 0 = 1047 over e to the power of (0.09 times 3 times 4)
b A LaTex expression showing S sub 0 = \frac{e to the power of (0.09 times 3 times 4) }{1047}
c A LaTex expression showing S sub 0 = 1047 over e to the power of (\frac{0.09 {3 over 4 )}}
5
A company's share price starts at a certain value. It grows continuously at 9% growth per month. After 3 quarters it has a share price of $261.
Rearrange the exponential equation to solve for for the starting price given this scenario?
a A LaTex expression showing S sub 0 = \frac{e to the power of (0.09 times 3 times 3) }{261}
b A LaTex expression showing S sub 0 = 261 over e to the power of (\frac{0.09 {3 over 3 )}}
c A LaTex expression showing S sub 0 = 261 over e to the power of (0.09 times 3 times 3)
6
A company's share price starts at a certain value. It grows continuously at 5% growth per month. After 6 quarters it has a share price of $269.
Rearrange the exponential equation to solve for for the starting price given this scenario?
a A LaTex expression showing S sub 0 = 269 over e to the power of (0.05 times 6 times 3)
b A LaTex expression showing S sub 0 = \frac{e to the power of (0.05 times 6 times 3) }{269}
7
A company's share price starts at a certain value. It grows continuously at 8% growth per quarter. After 3 years it has a share price of $889.
Rearrange the exponential equation to solve for for the starting price given this scenario?
a A LaTex expression showing S sub 0 = \frac{e to the power of (0.08 times 3 times 4) }{889}
b A LaTex expression showing S sub 0 = 889 over e to the power of (0.08 times 3 times 4)
8
An insect population starts at a certain size. It grows continuously at 5% growth per year. After 6 days it has increased to a population of 1,079.
Rearrange the exponential equation to solve for for the starting population given this scenario?
a A LaTex expression showing P sub 0 = e to the power of (0.05 times \frac{6 over 365 ) }{1079}
b A LaTex expression showing P sub 0 = 1079 over e to the power of (0.05 times \frac{6 {365 )}}
c A LaTex expression showing P sub 0 = 1079 over e to the power of (\frac{0.05 {6 times 365 )}}