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Exponential Function Solution Equation - Decay (Discrete) Scenario to Rate

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.

WorksheetView

Exponential Function Solution Equation - Decay (Discrete) Scenario to Rate Worksheet

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Exponential Function Solution Equation - Decay (Discrete) Scenario to...
1
A charitable endowment starts with $400. Each monthly it disburses a certain percent of its remaining funds. After 6 months its funds have decreased to $294.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = -(294 over 400 ) to the power of 1 over 6 - 1
b A LaTex expression showing r = -(294 over 400 ) to the power of 6 over 2 - 1
c A LaTex expression showing r = +(294 over 400 ) to the power of 1 over 6 + 1
2
A whale population starts at 300. Each subsequent year it declines by a certain percent. After 6 years it has decreased to a population of 265 whales.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = +(265 over 300 ) to the power of 1 over 6 + 1
b A LaTex expression showing r = -(265 over 300 ) to the power of 6 over 2 - 1
c A LaTex expression showing r = -(265 over 300 ) to the power of 1 over 6 - 1
3
A whale population starts at 800. Each subsequent year it declines by a certain percent. After 4 years it has decreased to a population of 598 whales.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = -(598 over 800 ) to the power of 1 over 4 - 1
b A LaTex expression showing r = +(598 over 800 ) to the power of 1 over 4 + 1
c A LaTex expression showing r = -(598 over 800 ) to the power of 4 over 2 - 1
4
A toxin starts at a concentration of 600mg/L. Each hourly dialysis reduces it by a certain percent. After 2 hours it has decreased to a concentration of 552mg/L.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = -(552 over 600 ) to the power of 1 over 2 - 1
b A LaTex expression showing r = +(552 over 600 ) to the power of 1 over 2 + 1
5
A charitable endowment starts with $600. Each monthly it disburses a certain percent of its remaining funds. After 9 months its funds have decreased to $415.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = -(415 over 600 ) to the power of 9 over 2 - 1
b A LaTex expression showing r = +(415 over 600 ) to the power of 1 over 9 + 1
c A LaTex expression showing r = -(415 over 600 ) to the power of 1 over 9 - 1
6
A bird population starts at 300. Each subsequent year it declines by a certain percent. After 8 years it has decreased to a population of 216.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = -(216 over 300 ) to the power of 8 over 2 - 1
b A LaTex expression showing r = -(216 over 300 ) to the power of 1 over 8 - 1
c A LaTex expression showing r = +(216 over 300 ) to the power of 1 over 8 + 1
7
A charitable endowment starts with $500. Each yearly it disburses a certain percent of its remaining funds. After 9 years its funds have decreased to $286.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = +(286 over 500 ) to the power of 1 over 9 + 1
b A LaTex expression showing r = -(286 over 500 ) to the power of 1 over 9 - 1
c A LaTex expression showing r = -(286 over 500 ) to the power of 9 over 2 - 1
8
A bird population starts at 300. Each subsequent year it declines by a certain percent. After 7 years it has decreased to a population of 209.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = -(209 over 300 ) to the power of 1 over 7 - 1
b A LaTex expression showing r = +(209 over 300 ) to the power of 1 over 7 + 1
c A LaTex expression showing r = -(209 over 300 ) to the power of 7 over 2 - 1