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

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Exponential Function Solution Equation - Decay (Discrete, Mis-matched...
1
A charitable endowment starts with a certain amount of money. Each daily it disburses 3% of its remaining funds. After 6 weeks its funds have decreased to $749.
Rearrange the exponential equation to solve for for the starting cash given this scenario?
a A LaTex expression showing P sub 0 = 749 over (1-0.03) to the power of 6 times 7
b A LaTex expression showing P sub 0 = 749 over (1+0.03) to the power of 6 times 7
c A LaTex expression showing P sub 0 = 749 times (1-0.03) to the power of 6 over 7
2
A charitable endowment starts with a certain amount of money. Each yearly it disburses 2% of its remaining funds. After 72 months its funds have decreased to $210.
Rearrange the exponential equation to solve for for the starting cash given this scenario?
a A LaTex expression showing P sub 0 = 210 over (1-0.02) to the power of \frac{72 {12 }}
b A LaTex expression showing P sub 0 = 210 over (1+0.02) to the power of \frac{72 {12 }}
3
A toxin starts at a certain concentration. Each daily dialysis reduces it by 5%. After 2 weeks it has decreased to a concentration of 631mg/L.
Rearrange the exponential equation to solve for for the starting concentration given this scenario?
a A LaTex expression showing C sub 0 = 631 over (1+0.05) to the power of 2 times 7
b A LaTex expression showing C sub 0 = 631 times (1-0.05) to the power of 2 over 7
c A LaTex expression showing C sub 0 = 631 over (1-0.05) to the power of 2 times 7
4
A charitable endowment starts with a certain amount of money. Each yearly it disburses 2% of its remaining funds. After 3285 days its funds have decreased to $0.
Rearrange the exponential equation to solve for for the starting cash given this scenario?
a A LaTex expression showing P sub 0 = 0 over (1+0.02) to the power of \frac{3285 {365 }}
b A LaTex expression showing P sub 0 = 0 times (1-0.02) to the power of 3285 times 365
c A LaTex expression showing P sub 0 = 0 over (1-0.02) to the power of \frac{3285 {365 }}
5
A charitable endowment starts with a certain amount of money. Each daily it disburses 3% of its remaining funds. After 5 weeks its funds have decreased to $686.
Rearrange the exponential equation to solve for for the starting cash given this scenario?
a A LaTex expression showing P sub 0 = 686 over (1+0.03) to the power of 5 times 7
b A LaTex expression showing P sub 0 = 686 times (1-0.03) to the power of 5 over 7
c A LaTex expression showing P sub 0 = 686 over (1-0.03) to the power of 5 times 7
6
A charitable endowment starts with a certain amount of money. Each yearly it disburses 4% of its remaining funds. After 2190 days its funds have decreased to $0.
Rearrange the exponential equation to solve for for the starting cash given this scenario?
a A LaTex expression showing P sub 0 = 0 times (1-0.04) to the power of 2190 times 365
b A LaTex expression showing P sub 0 = 0 over (1-0.04) to the power of \frac{2190 {365 }}
7
A toxin starts at a certain concentration. Each daily dialysis reduces it by 9%. After 8 weeks it has decreased to a concentration of 188mg/L.
Rearrange the exponential equation to solve for for the starting concentration given this scenario?
a A LaTex expression showing C sub 0 = 188 over (1-0.09) to the power of 8 times 7
b A LaTex expression showing C sub 0 = 188 over (1+0.09) to the power of 8 times 7
8
A charitable endowment starts with a certain amount of money. Each daily it disburses 6% of its remaining funds. After 2 weeks its funds have decreased to $265.
Rearrange the exponential equation to solve for for the starting cash given this scenario?
a A LaTex expression showing P sub 0 = 265 over (1+0.06) to the power of 2 times 7
b A LaTex expression showing P sub 0 = 265 over (1-0.06) to the power of 2 times 7
c A LaTex expression showing P sub 0 = 265 times (1-0.06) to the power of 2 over 7