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

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Exponential Function Solving - Growth (Discrete, Mis-matched Time Uni...
1
A savings account starts with $500. Each subsequent year it earns 8% in interest. After a certain number of quarters it has $4,313.
How would you solve for the time given this scenario?
a A LaTex expression showing t = 1 over 4 times \ln{\frac{P over P sub 0 }}{\ln{(1-r)}}
b A LaTex expression showing t = 4 times \ln{\frac{P over P sub 0 }}{\ln{(1+r)}}
c A LaTex expression showing t = 1 over 4 times \ln{\frac{P over P sub 0 }}{\ln{(1+r)}}
d A LaTex expression showing t = 4 times \frac{\ln{P times P sub 0 }}{\ln{(1+r)}}
2
A savings account starts with $400. Each subsequent month it earns 8% in interest. After a certain number of years it has $587.
How would you solve for the time given this scenario?
a A LaTex expression showing t = 12 times \ln{\frac{P over P sub 0 }}{\ln{(1+r)}}
b A LaTex expression showing t = 1 over 12 times \ln{\frac{P over P sub 0 }}{\ln{(1+r)}}
c A LaTex expression showing t = 1 over 12 times \frac{\ln{P times P sub 0 }}{\ln{(1+r)}}
3
A savings account starts with $300. Each subsequent year it earns 4% in interest. After a certain number of quarters it has $657.
How would you solve for the time given this scenario?
a A LaTex expression showing t = 1 over 4 times \ln{\frac{P over P sub 0 }}{\ln{(1+r)}}
b A LaTex expression showing t = 1 over 4 times \ln{\frac{P over P sub 0 }}{\ln{(1-r)}}
c A LaTex expression showing t = 4 times \ln{\frac{P over P sub 0 }}{\ln{(1+r)}}
4
A savings account starts with $400. Each subsequent month it earns 2% in interest. After a certain number of quarters it has $468.
How would you solve for the time given this scenario?
a A LaTex expression showing t = 1 over 3 times \ln{\frac{P over P sub 0 }}{\ln{(1+r)}}
b A LaTex expression showing t = 3 times \ln{\frac{P over P sub 0 }}{\ln{(1+r)}}
c A LaTex expression showing t = 1 over 3 times \frac{\ln{P times P sub 0 }}{\ln{(1+r)}}
5
A credit card starts with $500 of debt. Each subsequent quarter it grows by 4% in interest. After a certain number of months the debt has grown to $1,139.
How would you solve for the time given this scenario?
a A LaTex expression showing t = 1 over 3 times \ln{\frac{D over D sub 0 }}{\ln{(1+r)}}
b A LaTex expression showing t = 3 times \frac{\ln{D times D sub 0 }}{\ln{(1+r)}}
c A LaTex expression showing t = 3 times \ln{\frac{D over D sub 0 }}{\ln{(1+r)}}
d A LaTex expression showing t = 1 over 3 times \ln{\frac{D over D sub 0 }}{\ln{(1-r)}}
6
A credit card starts with $800 of debt. Each subsequent quarter it grows by 9% in interest. After a certain number of years the debt has grown to $1,036.
How would you solve for the time given this scenario?
a A LaTex expression showing t = 4 times \ln{\frac{D over D sub 0 }}{\ln{(1-r)}}
b A LaTex expression showing t = 4 times \ln{\frac{D over D sub 0 }}{\ln{(1+r)}}
c A LaTex expression showing t = 1 over 4 times \ln{\frac{D over D sub 0 }}{\ln{(1+r)}}
7
A credit card starts with $500 of debt. Each subsequent quarter it grows by 7% in interest. After a certain number of years the debt has grown to $859.
How would you solve for the time given this scenario?
a A LaTex expression showing t = 4 times \ln{\frac{D over D sub 0 }}{\ln{(1+r)}}
b A LaTex expression showing t = 4 times \ln{\frac{D over D sub 0 }}{\ln{(1-r)}}
c A LaTex expression showing t = 1 over 4 times \ln{\frac{D over D sub 0 }}{\ln{(1+r)}}
8
A credit card starts with $300 of debt. Each subsequent quarter it grows by 6% in interest. After a certain number of months the debt has grown to $1,019.
How would you solve for the time given this scenario?
a A LaTex expression showing t = 1 over 3 times \ln{\frac{D over D sub 0 }}{\ln{(1-r)}}
b A LaTex expression showing t = 3 times \ln{\frac{D over D sub 0 }}{\ln{(1+r)}}
c A LaTex expression showing t = 1 over 3 times \ln{\frac{D over D sub 0 }}{\ln{(1+r)}}