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Exponential Function Solution Equation - Decay (Discrete) Scenario to Starting Value

Level 1

The topics in this unit focus on understanding how to work with 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 - Decay (Discrete) Scenario to Starting Value Worksheet

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Exponential Function Solution Equation - Decay (Discrete) Scenario to...
1
A toxin starts at a certain concentration. Each monthly dialysis reduces it by 9%. After 6 months it has decreased to a concentration of 397mg/L.
Rearrange the exponential equation to solve for for the starting concentration given this scenario?
a A LaTex expression showing C sub 0 = 397 over (1-0.09) to the power of 6
b A LaTex expression showing C sub 0 = 397 times (1-0.09) to the power of 6
c A LaTex expression showing C sub 0 = 397 over (1+0.09) to the power of 6
2
A whale population starts at a certain size. Each subsequent year it declines by 5%. After 3 years it has decreased to a population of 514 whales.
Rearrange the exponential equation to solve for for the starting population given this scenario?
a A LaTex expression showing P sub 0 = 514 times (1-0.05) to the power of 3
b A LaTex expression showing P sub 0 = 514 over (1-0.05) to the power of 3
3
A bird population starts at a certain size. Each subsequent year it declines by 9%. After 7 years it has decreased to a population of 310.
Rearrange the exponential equation to solve for for the starting population given this scenario?
a A LaTex expression showing P sub 0 = 310 times (1-0.09) to the power of 7
b A LaTex expression showing P sub 0 = 310 over (1+0.09) to the power of 7
c A LaTex expression showing P sub 0 = 310 over (1-0.09) to the power of 7
4
A toxin starts at a certain concentration. Each daily dialysis reduces it by 8%. After 4 days it has decreased to a concentration of 644mg/L.
Rearrange the exponential equation to solve for for the starting concentration given this scenario?
a A LaTex expression showing C sub 0 = 644 times (1-0.08) to the power of 4
b A LaTex expression showing C sub 0 = 644 over (1+0.08) to the power of 4
c A LaTex expression showing C sub 0 = 644 over (1-0.08) to the power of 4
5
A whale population starts at a certain size. Each subsequent year it declines by 7%. After 8 years it has decreased to a population of 223 whales.
Rearrange the exponential equation to solve for for the starting population given this scenario?
a A LaTex expression showing P sub 0 = 223 over (1-0.07) to the power of 8
b A LaTex expression showing P sub 0 = 223 over (1+0.07) to the power of 8
6
A bird population starts at a certain size. Each subsequent year it declines by 4%. After 2 years it has decreased to a population of 460.
Rearrange the exponential equation to solve for for the starting population given this scenario?
a A LaTex expression showing P sub 0 = 460 over (1+0.04) to the power of 2
b A LaTex expression showing P sub 0 = 460 times (1-0.04) to the power of 2
c A LaTex expression showing P sub 0 = 460 over (1-0.04) to the power of 2
7
A whale population starts at a certain size. Each subsequent year it declines by 8%. After 2 years it has decreased to a population of 338 whales.
Rearrange the exponential equation to solve for for the starting population given this scenario?
a A LaTex expression showing P sub 0 = 338 times (1-0.08) to the power of 2
b A LaTex expression showing P sub 0 = 338 over (1+0.08) to the power of 2
c A LaTex expression showing P sub 0 = 338 over (1-0.08) to the power of 2
8
A charitable endowment starts with a certain amount of money. Each daily it disburses 3% of its remaining funds. After 2 days its funds have decreased to $752.
Rearrange the exponential equation to solve for for the starting cash given this scenario?
a A LaTex expression showing P sub 0 = 752 over (1-0.03) to the power of 2
b A LaTex expression showing P sub 0 = 752 times (1-0.03) to the power of 2
c A LaTex expression showing P sub 0 = 752 over (1+0.03) to the power of 2