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

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Exponential Function Solving - Decay (Discrete, Mis-matched Time Unit...
1
A toxin starts at a concentration of 300mg/L. Each hourly dialysis reduces it by a certain percent. After 5 days it has decreased to a concentration of 187mg/L.
How would you solve for the rate given this scenario?
a A LaTex expression showing r = -(C over C sub 0 ) to the power of t times 24 over 2 - 1
b A LaTex expression showing r = -(C over C sub 0 ) to the power of 1 over t times 24 - 1
2
A charitable endowment starts with $400. Each daily it disburses a certain percent of its remaining funds. After 2 years its funds have decreased to $361.
How would you 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 times 365 - 1
b A LaTex expression showing r = -(P over P sub 0 ) to the power of t times 365 over 2 - 1
c A LaTex expression showing r = -(P over P sub 0 ) to the power of 1 over \frac{t {365 } } + 1
3
A toxin starts at a concentration of 400mg/L. Each weekly dialysis reduces it by a certain percent. After 14 days it has decreased to a concentration of 144mg/L.
How would you solve for the rate given this scenario?
a A LaTex expression showing r = -(C over C sub 0 ) to the power of 1 over \frac{t {7 } } - 1
b A LaTex expression showing r = -(C over C sub 0 ) to the power of 1 over t times 7 + 1
c A LaTex expression showing r = -(C over C sub 0 ) to the power of \frac{t over 7 {2} } - 1
4
A toxin starts at a concentration of 500mg/L. Each daily dialysis reduces it by a certain percent. After 9 weeks it has decreased to a concentration of 346mg/L.
How would you solve for the rate given this scenario?
a A LaTex expression showing r = -(C over C sub 0 ) to the power of t times 7 over 2 - 1
b A LaTex expression showing r = -(C over C sub 0 ) to the power of 1 over \frac{t {7 } } + 1
c A LaTex expression showing r = -(C over C sub 0 ) to the power of 1 over t times 7 - 1
5
A charitable endowment starts with $800. Each yearly it disburses a certain percent of its remaining funds. After 1095 days its funds have decreased to $0.
How would you 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 times 365 + 1
b A LaTex expression showing r = -(P over P sub 0 ) to the power of 1 over \frac{t {365 } } - 1
c A LaTex expression showing r = -(P over P sub 0 ) to the power of \frac{t over 365 {2} } - 1
6
A charitable endowment starts with $300. Each daily it disburses a certain percent of its remaining funds. After 6 years its funds have decreased to $220.
How would you solve for the rate given this scenario?
a A LaTex expression showing r = -(P over P sub 0 ) to the power of t times 365 over 2 - 1
b A LaTex expression showing r = -(P over P sub 0 ) to the power of 1 over t times 365 - 1
c A LaTex expression showing r = -(P over P sub 0 ) to the power of 1 over \frac{t {365 } } + 1
7
A toxin starts at a concentration of 600mg/L. Each weekly dialysis reduces it by a certain percent. After 14 days it has decreased to a concentration of 186mg/L.
How would you solve for the rate given this scenario?
a A LaTex expression showing r = -(C over C sub 0 ) to the power of 1 over t times 7 + 1
b A LaTex expression showing r = -(C over C sub 0 ) to the power of 1 over \frac{t {7 } } - 1
c A LaTex expression showing r = -(C over C sub 0 ) to the power of \frac{t over 7 {2} } - 1
8
A charitable endowment starts with $800. Each weekly it disburses a certain percent of its remaining funds. After 14 days its funds have decreased to $289.
How would you solve for the rate given this scenario?
a A LaTex expression showing r = -(P over P sub 0 ) to the power of 1 over \frac{t {7 } } - 1
b A LaTex expression showing r = -(P over P sub 0 ) to the power of \frac{t over 7 {2} } - 1
c A LaTex expression showing r = -(P over P sub 0 ) to the power of 1 over t times 7 + 1