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Exponential Function Solution Equation - Growth (Continuous) - Equation to Time

Level 1

This topic is designed to practice solving for time in models of continuous exponential growth within various contexts, such as social media post views, bacteria population growth, rabbit population growth, credit card debt, and money growth in savings accounts. It involves rearranging exponential functions to isolate and solve for the variable representing time, using logarithmic manipulations. These types of problems help enhance the understanding of exponential functions and their real-world applications.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Exponential Function Solution Equation - Growth (Continuous) - Equation to Time Worksheet

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Exponential Function Solution Equation - Growth (Continuous) - Equati...
1
Rearrange this equation to solve for the time given this model of a continuous exponential growth of social media post views?
A LaTex expression showing 1,372 =800 times e to the power of (0.06 times t)
a A LaTex expression showing t = +\ln{\frac{1372 over 800 }}{0.06}
b A LaTex expression showing t = -\frac{\ln{1372 times 800}}{0.06}
c A LaTex expression showing t = +0.06 over \ln{\frac{1372 {800}}}
2
Rearrange this equation to solve for the time given this model of a continuous growth of a bacteria population?
A LaTex expression showing 525 =300 times e to the power of (0.08 times t)
a A LaTex expression showing t = -\frac{\ln{525 times 300}}{0.08}
b A LaTex expression showing t = +\ln{\frac{525 over 300 }}{0.08}
c A LaTex expression showing t = +0.08 over \ln{\frac{525 {300}}}
3
Rearrange this equation to solve for the time given this model of a continuous exponential growth of social media post views?
A LaTex expression showing 1,369 =900 times e to the power of (0.07 times t)
a A LaTex expression showing t = -\frac{\ln{1369 times 900}}{0.07}
b A LaTex expression showing t = +0.07 over \ln{\frac{1369 {900}}}
c A LaTex expression showing t = +\ln{\frac{1369 over 900 }}{0.07}
4
Rearrange this equation to solve for the time given this model of a continuous growth of a rabbit population?
A LaTex expression showing 598 =500 times e to the power of (0.06 times t)
a A LaTex expression showing t = +\ln{\frac{598 over 500 }}{0.06}
b A LaTex expression showing t = -\frac{\ln{598 times 500}}{0.06}
5
Rearrange this equation to solve for the time given this model of a continuous exponential growth of social media post views?
A LaTex expression showing 1,144 =900 times e to the power of (0.08 times t)
a A LaTex expression showing t = +\ln{\frac{1144 over 900 }}{0.08}
b A LaTex expression showing t = -\frac{\ln{1144 times 900}}{0.08}
c A LaTex expression showing t = +0.08 over \ln{\frac{1144 {900}}}
6
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 1,016 =800 times e to the power of (0.04 times t)
a A LaTex expression showing t = +\ln{\frac{1016 over 800 }}{0.04}
b A LaTex expression showing t = +0.04 over \ln{\frac{1016 {800}}}
c A LaTex expression showing t = -\frac{\ln{1016 times 800}}{0.04}
7
Rearrange this equation to solve for the time given this model of a continuously compounding growth of money in a savings account?
A LaTex expression showing 1,035 =900 times e to the power of (0.02 times t)
a A LaTex expression showing t = -\frac{\ln{1035 times 900}}{0.02}
b A LaTex expression showing t = +\ln{\frac{1035 over 900 }}{0.02}
8
Rearrange this equation to solve for the time given this model of a continuous exponential growth of social media post views?
A LaTex expression showing 1,232 =600 times e to the power of (0.09 times t)
a A LaTex expression showing t = -\frac{\ln{1232 times 600}}{0.09}
b A LaTex expression showing t = +\ln{\frac{1232 over 600 }}{0.09}