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Exponential Function Solving - Decay (Discrete) Scenario to Rate

Level 1

This math topic focuses on solving exponential decay problems in discrete scenarios by finding the rate of decay given specific starting and ending values over a particular time frame. The examples provided include scenarios involving toxin concentrations, bird populations, charitable endowments, and whale populations, among others. Each problem requires deducing the exponential decay rate from provided data, integrating real-life applications of exponential functions into the exercises.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Exponential Function Solving - Decay (Discrete) Scenario to Rate Worksheet

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Exponential Function Solving - Decay (Discrete) Scenario to Rate
1
A toxin starts at a concentration of 600mg/L. Each hourly dialysis reduces it by a certain percent. After 8 hours it has decreased to a concentration of 282mg/L.
Solve for the rate given this scenario?
a A LaTex expression showing 7 + r = -(C over C sub 0 ) to the power of 1 over t + 1
b A LaTex expression showing 7 + r = -(C over C sub 0 ) to the power of t over 2 - 1
c A LaTex expression showing r = -(C over C sub 0 ) to the power of 1 over t - 1
2
A charitable endowment starts with $200. Each daily it disburses a certain percent of its remaining funds. After 4 days its funds have decreased to $156.
Solve for the rate given this scenario?
a A LaTex expression showing r = -(P over P sub 0 ) to the power of 1 over t - 1
b A LaTex expression showing 4 + r = -(P over P sub 0 ) to the power of t over 2 - 1
c A LaTex expression showing 2 + r = -(P over P sub 0 ) to the power of 1 over t + 1
3
A bird population starts at 500. Each subsequent year it declines by a certain percent. After 7 years it has decreased to a population of 258.
Solve for the rate given this scenario?
a A LaTex expression showing 6 + r = -(P over P sub 0 ) to the power of 1 over t + 1
b A LaTex expression showing 8 + r = -(P over P sub 0 ) to the power of 1 over t + 1
c A LaTex expression showing r = -(P over P sub 0 ) to the power of 1 over t - 1
4
A bird population starts at 900. Each subsequent year it declines by a certain percent. After 7 years it has decreased to a population of 676.
Solve for the rate given this scenario?
a A LaTex expression showing 0 + r = -(P over P sub 0 ) to the power of t over 2 - 1
b A LaTex expression showing r = -(P over P sub 0 ) to the power of 1 over t - 1
c A LaTex expression showing 0 + r = -(P over P sub 0 ) to the power of 1 over t + 1
d A LaTex expression showing 6 + r = -(P over P sub 0 ) to the power of t over 2 - 1
5
A charitable endowment starts with $900. Each monthly it disburses a certain percent of its remaining funds. After 5 months its funds have decreased to $733.
Solve for the rate given this scenario?
a A LaTex expression showing 2 + r = -(P over P sub 0 ) to the power of t over 2 - 1
b A LaTex expression showing 7 + r = -(P over P sub 0 ) to the power of 1 over t + 1
c A LaTex expression showing 7 + r = -(P over P sub 0 ) to the power of t over 2 - 1
d A LaTex expression showing r = -(P over P sub 0 ) to the power of 1 over t - 1
6
A whale population starts at 300. Each subsequent year it declines by a certain percent. After 5 years it has decreased to a population of 271 whales.
Solve for the rate given this scenario?
a A LaTex expression showing r = -(P over P sub 0 ) to the power of 1 over t - 1
b A LaTex expression showing 3 + r = -(P over P sub 0 ) to the power of 1 over t + 1
c A LaTex expression showing 9 + r = -(P over P sub 0 ) to the power of t over 2 - 1
d A LaTex expression showing 7 + r = -(P over P sub 0 ) to the power of 1 over t + 1
7
A whale population starts at 600. Each subsequent year it declines by a certain percent. After 4 years it has decreased to a population of 531 whales.
Solve for the rate given this scenario?
a A LaTex expression showing r = -(P over P sub 0 ) to the power of 1 over t - 1
b A LaTex expression showing 9 + r = -(P over P sub 0 ) to the power of t over 2 - 1
c A LaTex expression showing 6 + r = -(P over P sub 0 ) to the power of 1 over t + 1
d A LaTex expression showing 2 + r = -(P over P sub 0 ) to the power of 1 over t + 1
8
A charitable endowment starts with $500. Each daily it disburses a certain percent of its remaining funds. After 6 days its funds have decreased to $323.
Solve for the rate given this scenario?
a A LaTex expression showing 6 + r = -(P over P sub 0 ) to the power of 1 over t + 1
b A LaTex expression showing 1 + r = -(P over P sub 0 ) to the power of t over 2 - 1
c A LaTex expression showing 5 + r = -(P over P sub 0 ) to the power of 1 over t + 1
d A LaTex expression showing r = -(P over P sub 0 ) to the power of 1 over t - 1