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

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 Time Worksheet

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Exponential Function Solving - Decay (Discrete, Mis-matched Time Unit...
1
A charitable endowment starts with $600. Each weekly it disburses 9% of its remaining funds. After a certain number of days its funds have decreased to $82.
How would you solve for the time given this scenario?
a A LaTex expression showing t = 1 over 7 times \ln{\frac{P over P sub 0 }}{\ln{(1+r)}}
b A LaTex expression showing t = 7 times \ln{\frac{P over P sub 0 }}{\ln{(1-r)}}
c A LaTex expression showing t = 7 times \frac{\ln{P times P sub 0 }}{\ln{(1-r)}}
2
A charitable endowment starts with $600. Each yearly it disburses 8% of its remaining funds. After a certain number of months its funds have decreased to $0.
How would you solve for the time given this scenario?
a A LaTex expression showing t = 1 over 12 times \ln{\frac{P over P sub 0 }}{\ln{(1-r)}}
b A LaTex expression showing t = 12 times \ln{\frac{P over P sub 0 }}{\ln{(1-r)}}
3
A charitable endowment starts with $700. Each yearly it disburses 9% of its remaining funds. After a certain number of days its funds have decreased to $0.
How would you solve for the time given this scenario?
a A LaTex expression showing t = 365 times \frac{\ln{P times P sub 0 }}{\ln{(1-r)}}
b A LaTex expression showing t = 1 over 365 times \ln{\frac{P over P sub 0 }}{\ln{(1+r)}}
c A LaTex expression showing t = 1 over 365 times \ln{\frac{P over P sub 0 }}{\ln{(1-r)}}
d A LaTex expression showing t = 365 times \ln{\frac{P over P sub 0 }}{\ln{(1-r)}}
4
A toxin starts at a concentration of 900mg/L. Each daily dialysis reduces it by 4%. After a certain number of hours it has decreased to a concentration of 47mg/L.
How would you solve for the time given this scenario?
a A LaTex expression showing t = 24 times \ln{\frac{C over C sub 0 }}{\ln{(1-r)}}
b A LaTex expression showing t = 1 over 24 times \ln{\frac{C over C sub 0 }}{\ln{(1-r)}}
c A LaTex expression showing t = 1 over 24 times \ln{\frac{C over C sub 0 }}{\ln{(1+r)}}
5
A charitable endowment starts with $300. Each monthly it disburses 7% of its remaining funds. After a certain number of years its funds have decreased to $224.
How would you solve for the time given this scenario?
a A LaTex expression showing t = 1 over 12 times \frac{\ln{P times P sub 0 }}{\ln{(1-r)}}
b A LaTex expression showing t = 12 times \ln{\frac{P over P sub 0 }}{\ln{(1-r)}}
c A LaTex expression showing t = 1 over 12 times \ln{\frac{P over P sub 0 }}{\ln{(1-r)}}
6
A charitable endowment starts with $200. Each yearly it disburses 8% of its remaining funds. After a certain number of days its funds have decreased to $0.
How would you solve for the time given this scenario?
a A LaTex expression showing t = 365 times \frac{\ln{P times P sub 0 }}{\ln{(1-r)}}
b A LaTex expression showing t = 365 times \ln{\frac{P over P sub 0 }}{\ln{(1-r)}}
7
A charitable endowment starts with $600. Each daily it disburses 2% of its remaining funds. After a certain number of weeks its funds have decreased to $553.
How would you solve for the time given this scenario?
a A LaTex expression showing t = 1 over 7 times \ln{\frac{P over P sub 0 }}{\ln{(1-r)}}
b A LaTex expression showing t = 7 times \ln{\frac{P over P sub 0 }}{\ln{(1+r)}}
8
A toxin starts at a concentration of 600mg/L. Each daily dialysis reduces it by 4%. After a certain number of hours it has decreased to a concentration of 31mg/L.
How would you solve for the time given this scenario?
a A LaTex expression showing t = 24 times \ln{\frac{C over C sub 0 }}{\ln{(1-r)}}
b A LaTex expression showing t = 24 times \frac{\ln{C times C sub 0 }}{\ln{(1-r)}}
c A LaTex expression showing t = 1 over 24 times \ln{\frac{C over C sub 0 }}{\ln{(1+r)}}