Exponential Function Solution Equation - Decay (Discrete, Mis-matched Time Units) - Equation 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.

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

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Exponential Function Solution Equation - Decay (Discrete, Mis-matched...
1
Rearrange this equation to solve for the time given this model of a balance of a charitable endowment (weekly disbursements)?
A LaTex expression showing 186 =700 times (1-0.09) to the power of (t over 7 )
a A LaTex expression showing t = 7 times \frac{\ln{186 times 700}}{\ln{(1-0.09)}}
b A LaTex expression showing t = 1 over 7 times \ln{\frac{186 over 700 }}{\ln{(1+0.09)}}
c A LaTex expression showing t = 7 times \ln{\frac{186 over 700 }}{\ln{(1-0.09)}}
d A LaTex expression showing t = 1 over 7 times \ln{\frac{186 over 700 }}{\ln{(1-0.09)}}
2
Rearrange this equation to solve for the time given this model of a decline of a toxin concentration (daily dialysis)?
A LaTex expression showing 4 =900 times (1-0.07) to the power of (t over 24 )
a A LaTex expression showing t = 24 times \ln{\frac{4 over 900 }}{\ln{(1-0.07)}}
b A LaTex expression showing t = 24 times \frac{\ln{4 times 900}}{\ln{(1-0.07)}}
c A LaTex expression showing t = 1 over 24 times \ln{\frac{4 over 900 }}{\ln{(1+0.07)}}
d A LaTex expression showing t = 1 over 24 times \ln{\frac{4 over 900 }}{\ln{(1-0.07)}}
3
Rearrange this equation to solve for the time given this model of a balance of a charitable endowment (daily disbursements)?
A LaTex expression showing 413 =800 times (1-0.09) to the power of (t times 365)
a A LaTex expression showing t = 1 over 365 times \ln{\frac{413 over 800 }}{\ln{(1-0.09)}}
b A LaTex expression showing t = 1 over 365 times \frac{\ln{413 times 800}}{\ln{(1-0.09)}}
c A LaTex expression showing t = 365 times \ln{\frac{413 over 800 }}{\ln{(1-0.09)}}
d A LaTex expression showing t = 365 times \ln{\frac{413 over 800 }}{\ln{(1+0.09)}}
4
Rearrange this equation to solve for the time given this model of a balance of a charitable endowment (yearly disbursements)?
A LaTex expression showing 0 =200 times (1-0.09) to the power of (t over 365 )
a A LaTex expression showing t = 365 times \ln{\frac{0 over 200 }}{\ln{(1-0.09)}}
b A LaTex expression showing t = 1 over 365 times \ln{\frac{0 over 200 }}{\ln{(1-0.09)}}
c A LaTex expression showing t = 365 times \frac{\ln{0 times 200}}{\ln{(1-0.09)}}
d A LaTex expression showing t = 1 over 365 times \ln{\frac{0 over 200 }}{\ln{(1+0.09)}}
5
Rearrange this equation to solve for the time given this model of a decline of a toxin concentration (hourly dialysis)?
A LaTex expression showing 278 =400 times (1-0.07) to the power of (t times 24)
a A LaTex expression showing t = 24 times \ln{\frac{278 over 400 }}{\ln{(1+0.07)}}
b A LaTex expression showing t = 24 times \ln{\frac{278 over 400 }}{\ln{(1-0.07)}}
c A LaTex expression showing t = 1 over 24 times \ln{\frac{278 over 400 }}{\ln{(1-0.07)}}
d A LaTex expression showing t = 1 over 24 times \frac{\ln{278 times 400}}{\ln{(1-0.07)}}
6
Rearrange this equation to solve for the time given this model of a balance of a charitable endowment (yearly disbursements)?
A LaTex expression showing 0 =600 times (1-0.08) to the power of (t over 12 )
a A LaTex expression showing t = 1 over 12 times \ln{\frac{0 over 600 }}{\ln{(1+0.08)}}
b A LaTex expression showing t = 1 over 12 times \ln{\frac{0 over 600 }}{\ln{(1-0.08)}}
c A LaTex expression showing t = 12 times \ln{\frac{0 over 600 }}{\ln{(1-0.08)}}
7
Rearrange this equation to solve for the time given this model of a decline of a toxin concentration (weekly dialysis)?
A LaTex expression showing 133 =500 times (1-0.09) to the power of (t over 7 )
a A LaTex expression showing t = 7 times \ln{\frac{133 over 500 }}{\ln{(1-0.09)}}
b A LaTex expression showing t = 7 times \frac{\ln{133 times 500}}{\ln{(1-0.09)}}
c A LaTex expression showing t = 1 over 7 times \ln{\frac{133 over 500 }}{\ln{(1-0.09)}}
8
Rearrange this equation to solve for the time given this model of a balance of a charitable endowment (yearly disbursements)?
A LaTex expression showing 0 =900 times (1-0.03) to the power of (t over 365 )
a A LaTex expression showing t = 365 times \ln{\frac{0 over 900 }}{\ln{(1-0.03)}}
b A LaTex expression showing t = 1 over 365 times \ln{\frac{0 over 900 }}{\ln{(1+0.03)}}
c A LaTex expression showing t = 1 over 365 times \ln{\frac{0 over 900 }}{\ln{(1-0.03)}}