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

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.

WorksheetView

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

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Exponential Function Solution Equation - Decay (Discrete, Mis-matched...
1
A charitable endowment starts with $600. Each monthly it disburses a certain percent of its remaining funds. After 9 years its funds have decreased to $283.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = +(283 over 600 ) to the power of 1 over \frac{9 {12 } } + 1
b A LaTex expression showing r = -(283 over 600 ) to the power of 9 times 12 over 2 - 1
c A LaTex expression showing r = -(283 over 600 ) to the power of 1 over 9 times 12 - 1
2
A toxin starts at a concentration of 300mg/L. Each daily dialysis reduces it by a certain percent. After 4 weeks it has decreased to a concentration of 224mg/L.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = +(224 over 300 ) to the power of 1 over \frac{4 {7 } } + 1
b A LaTex expression showing r = -(224 over 300 ) to the power of 4 times 7 over 2 - 1
c A LaTex expression showing r = -(224 over 300 ) to the power of 1 over 4 times 7 - 1
3
A toxin starts at a concentration of 200mg/L. Each hourly dialysis reduces it by a certain percent. After 4 days it has decreased to a concentration of 143mg/L.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = -(143 over 200 ) to the power of 4 times 24 over 2 - 1
b A LaTex expression showing r = -(143 over 200 ) to the power of 1 over 4 times 24 - 1
4
A charitable endowment starts with $200. Each weekly it disburses a certain percent of its remaining funds. After 28 days its funds have decreased to $19.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = -(19 over 200 ) to the power of 1 over \frac{28 {7 } } - 1
b A LaTex expression showing r = +(19 over 200 ) to the power of 1 over 28 times 7 + 1
c A LaTex expression showing r = -(19 over 200 ) to the power of \frac{28 over 7 {2} } - 1
5
A toxin starts at a concentration of 700mg/L. Each daily dialysis reduces it by a certain percent. After 5 weeks it has decreased to a concentration of 436mg/L.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = -(436 over 700 ) to the power of 5 times 7 over 2 - 1
b A LaTex expression showing r = -(436 over 700 ) to the power of 1 over 5 times 7 - 1
c A LaTex expression showing r = +(436 over 700 ) to the power of 1 over \frac{5 {7 } } + 1
6
A charitable endowment starts with $300. Each monthly it disburses a certain percent of its remaining funds. After 9 years its funds have decreased to $189.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = -(189 over 300 ) to the power of 9 times 12 over 2 - 1
b A LaTex expression showing r = -(189 over 300 ) to the power of 1 over 9 times 12 - 1
c A LaTex expression showing r = +(189 over 300 ) to the power of 1 over \frac{9 {12 } } + 1
7
A charitable endowment starts with $800. Each daily it disburses a certain percent of its remaining funds. After 3 weeks its funds have decreased to $752.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = -(752 over 800 ) to the power of 3 times 7 over 2 - 1
b A LaTex expression showing r = -(752 over 800 ) to the power of 1 over 3 times 7 - 1
8
A toxin starts at a concentration of 800mg/L. Each daily dialysis reduces it by a certain percent. After 4 weeks it has decreased to a concentration of 737mg/L.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = -(737 over 800 ) to the power of 1 over 4 times 7 - 1
b A LaTex expression showing r = +(737 over 800 ) to the power of 1 over \frac{4 {7 } } + 1
c A LaTex expression showing r = -(737 over 800 ) to the power of 4 times 7 over 2 - 1