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

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Exponential Function Solution Equation - Growth (Continuous, Mis-matc...
1
Rearrange this equation to solve for the time given this model of a growth of debt on a credit card with continuous compounding?
A LaTex expression showing 298 =200 times e to the power of (0.08 times t over 12 )
a A LaTex expression showing t = -1 over 12 times \frac{\ln{298 times 200}}{0.08}
b A LaTex expression showing t = 12 times 0.08 over \ln{\frac{298 {200}}}
c A LaTex expression showing t = 12 times \ln{\frac{298 over 200 }}{0.08}
2
Rearrange this equation to solve for the time given this model of a continuous growth of a bacteria population?
A LaTex expression showing 697 =600 times e to the power of (0.05 times t times 7)
a A LaTex expression showing t = -7 times \frac{\ln{697 times 600}}{0.05}
b A LaTex expression showing t = 1 over 7 times 0.05 over \ln{\frac{697 {600}}}
c A LaTex expression showing t = 1 over 7 times \ln{\frac{697 over 600 }}{0.05}
3
Rearrange this equation to solve for the time given this model of a continuously compounding growth of a share price?
A LaTex expression showing 1,014 =900 times e to the power of (0.06 times t over 3 )
a A LaTex expression showing t = 3 times \ln{\frac{1014 over 900 }}{0.06}
b A LaTex expression showing t = -1 over 3 times \frac{\ln{1014 times 900}}{0.06}
c A LaTex expression showing t = 3 times 0.06 over \ln{\frac{1014 {900}}}
4
Rearrange this equation to solve for the time given this model of a continuously compounding growth of a share price?
A LaTex expression showing 425 =300 times e to the power of (0.05 times t times 3)
a A LaTex expression showing t = 1 over 3 times 0.05 over \ln{\frac{425 {300}}}
b A LaTex expression showing t = 1 over 3 times \ln{\frac{425 over 300 }}{0.05}
c A LaTex expression showing t = 3 times \ln{\frac{425 over 300 }}{0.05}
d A LaTex expression showing t = -3 times \frac{\ln{425 times 300}}{0.05}
5
Rearrange this equation to solve for the time given this model of a continuously compounding growth of app downloads?
A LaTex expression showing 854 =700 times e to the power of (0.04 times t over 7 )
a A LaTex expression showing t = -1 over 7 times \frac{\ln{854 times 700}}{0.04}
b A LaTex expression showing t = 1 over 7 times \ln{\frac{854 over 700 }}{0.04}
c A LaTex expression showing t = 7 times \ln{\frac{854 over 700 }}{0.04}
d A LaTex expression showing t = 7 times 0.04 over \ln{\frac{854 {700}}}
6
Rearrange this equation to solve for the time given this model of a continuous growth of an insect population?
A LaTex expression showing 563 =500 times e to the power of (0.06 times t over 7 )
a A LaTex expression showing t = -1 over 7 times \frac{\ln{563 times 500}}{0.06}
b A LaTex expression showing t = 7 times 0.06 over \ln{\frac{563 {500}}}
c A LaTex expression showing t = 1 over 7 times \ln{\frac{563 over 500 }}{0.06}
d A LaTex expression showing t = 7 times \ln{\frac{563 over 500 }}{0.06}
7
Rearrange this equation to solve for the time given this model of a growth of debt on a credit card with continuous compounding?
A LaTex expression showing 901 =800 times e to the power of (0.04 times t times 3)
a A LaTex expression showing t = 1 over 3 times 0.04 over \ln{\frac{901 {800}}}
b A LaTex expression showing t = 3 times \ln{\frac{901 over 800 }}{0.04}
c A LaTex expression showing t = -3 times \frac{\ln{901 times 800}}{0.04}
d A LaTex expression showing t = 1 over 3 times \ln{\frac{901 over 800 }}{0.04}
8
Rearrange this equation to solve for the time given this model of a continuously compounding growth of a share price?
A LaTex expression showing 523 =400 times e to the power of (0.09 times t over 3 )
a A LaTex expression showing t = -1 over 3 times \frac{\ln{523 times 400}}{0.09}
b A LaTex expression showing t = 3 times \ln{\frac{523 over 400 }}{0.09}
c A LaTex expression showing t = 1 over 3 times \ln{\frac{523 over 400 }}{0.09}
d A LaTex expression showing t = 3 times 0.09 over \ln{\frac{523 {400}}}