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Exponential Function Solution Equation - 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.

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

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Exponential Function Solution Equation - Growth (Discrete, Mis-matche...
1
A credit card starts with $400 of debt. Each subsequent quarter it grows by 3% in interest. After a certain number of years the debt has grown to $477.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = 4 times \ln{\frac{477 over 400 }}{\ln{(1+0.03)}}
b A LaTex expression showing t = 1 over 4 times \frac{\ln{477 times 400}}{\ln{(1+0.03)}}
c A LaTex expression showing t = 1 over 4 times \ln{\frac{477 over 400 }}{\ln{(1+0.03)}}
2
A credit card starts with $600 of debt. Each subsequent quarter it grows by 7% in interest. After a certain number of years the debt has grown to $1,103.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = 1 over 4 times \frac{\ln{1103 times 600}}{\ln{(1+0.07)}}
b A LaTex expression showing t = 4 times \ln{\frac{1103 over 600 }}{\ln{(1-0.07)}}
c A LaTex expression showing t = 1 over 4 times \ln{\frac{1103 over 600 }}{\ln{(1+0.07)}}
3
A savings account starts with $600. Each subsequent quarter it earns 8% in interest. After a certain number of months it has $1,510.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = 3 times \frac{\ln{1510 times 600}}{\ln{(1+0.08)}}
b A LaTex expression showing t = 1 over 3 times \ln{\frac{1510 over 600 }}{\ln{(1-0.08)}}
c A LaTex expression showing t = 3 times \ln{\frac{1510 over 600 }}{\ln{(1+0.08)}}
4
A savings account starts with $900. Each subsequent year it earns 4% in interest. After a certain number of months it has $38,854.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = 1 over 12 times \ln{\frac{38854 over 900 }}{\ln{(1-0.04)}}
b A LaTex expression showing t = 12 times \ln{\frac{38854 over 900 }}{\ln{(1+0.04)}}
5
A savings account starts with $700. Each subsequent year it earns 4% in interest. After a certain number of months it has $1,794.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = 12 times \frac{\ln{1794 times 700}}{\ln{(1+0.04)}}
b A LaTex expression showing t = 12 times \ln{\frac{1794 over 700 }}{\ln{(1+0.04)}}
c A LaTex expression showing t = 1 over 12 times \ln{\frac{1794 over 700 }}{\ln{(1+0.04)}}
d A LaTex expression showing t = 1 over 12 times \ln{\frac{1794 over 700 }}{\ln{(1-0.04)}}
6
A credit card starts with $800 of debt. Each subsequent month it grows by 4% in interest. After a certain number of years the debt has grown to $865.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = 12 times \ln{\frac{865 over 800 }}{\ln{(1-0.04)}}
b A LaTex expression showing t = 12 times \ln{\frac{865 over 800 }}{\ln{(1+0.04)}}
c A LaTex expression showing t = 1 over 12 times \ln{\frac{865 over 800 }}{\ln{(1+0.04)}}
7
A credit card starts with $800 of debt. Each subsequent year it grows by 9% in interest. After a certain number of quarters the debt has grown to $4,483.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = 4 times \frac{\ln{4483 times 800}}{\ln{(1+0.09)}}
b A LaTex expression showing t = 1 over 4 times \ln{\frac{4483 over 800 }}{\ln{(1-0.09)}}
c A LaTex expression showing t = 4 times \ln{\frac{4483 over 800 }}{\ln{(1+0.09)}}
d A LaTex expression showing t = 1 over 4 times \ln{\frac{4483 over 800 }}{\ln{(1+0.09)}}
8
A savings account starts with $600. Each subsequent year it earns 7% in interest. After a certain number of months it has $34,767.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = 12 times \ln{\frac{34767 over 600 }}{\ln{(1+0.07)}}
b A LaTex expression showing t = 1 over 12 times \ln{\frac{34767 over 600 }}{\ln{(1+0.07)}}