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

Level 1

This math topic focuses on solving for time in equations representing continuous decay processes, such as decreasing bacteria populations or radioactive material decay. The problems involve rearranging exponential decay equations to isolate and calculate the variable 't' (time), using properties of logarithms and exponentials. Each problem contains an exponential equation with different parameters and offers multiple-choice solutions for students to select the correct rearrangement. These types of problems are an introductory exploration into exponential functions.

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

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

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Exponential Function Solution Equation - Decay (Continuous) - Equatio...
1
Rearrange this equation to solve for the time given this model of a a continuously declining bacteria population?
A LaTex expression showing 521 =600 times e to the power of (-0.02 times t)
a A LaTex expression showing t = -\ln{\frac{521 over 600 }}{0.02}
b A LaTex expression showing t = -0.02 over \ln{\frac{521 {600}}}
c A LaTex expression showing t = +\frac{\ln{521 times 600}}{0.02}
2
Rearrange this equation to solve for the time given this model of a a continuously declining bacteria population?
A LaTex expression showing 222 =300 times e to the power of (-0.06 times t)
a A LaTex expression showing t = -0.06 over \ln{\frac{222 {300}}}
b A LaTex expression showing t = +\frac{\ln{222 times 300}}{0.06}
c A LaTex expression showing t = -\ln{\frac{222 over 300 }}{0.06}
3
Rearrange this equation to solve for the time given this model of a continuous decay of a radioactive material?
A LaTex expression showing 847 =900 times e to the power of (-0.03 times t)
a A LaTex expression showing t = +\frac{\ln{847 times 900}}{0.03}
b A LaTex expression showing t = -\ln{\frac{847 over 900 }}{0.03}
c A LaTex expression showing t = -0.03 over \ln{\frac{847 {900}}}
4
Rearrange this equation to solve for the time given this model of a continuous decay of a radioactive material?
A LaTex expression showing 197 =300 times e to the power of (-0.06 times t)
a A LaTex expression showing t = -\ln{\frac{197 over 300 }}{0.06}
b A LaTex expression showing t = +\frac{\ln{197 times 300}}{0.06}
c A LaTex expression showing t = -0.06 over \ln{\frac{197 {300}}}
5
Rearrange this equation to solve for the time given this model of a a continuously declining bacteria population?
A LaTex expression showing 334 =400 times e to the power of (-0.03 times t)
a A LaTex expression showing t = -\ln{\frac{334 over 400 }}{0.03}
b A LaTex expression showing t = +\frac{\ln{334 times 400}}{0.03}
c A LaTex expression showing t = -0.03 over \ln{\frac{334 {400}}}
6
Rearrange this equation to solve for the time given this model of a continuous reduction of a toxin concentration?
A LaTex expression showing 433 =700 times e to the power of (-0.08 times t)
a A LaTex expression showing t = -\ln{\frac{433 over 700 }}{0.08}
b A LaTex expression showing t = +\frac{\ln{433 times 700}}{0.08}
c A LaTex expression showing t = -0.08 over \ln{\frac{433 {700}}}
7
Rearrange this equation to solve for the time given this model of a continuous decay of a radioactive material?
A LaTex expression showing 738 =800 times e to the power of (-0.02 times t)
a A LaTex expression showing t = -\ln{\frac{738 over 800 }}{0.02}
b A LaTex expression showing t = -0.02 over \ln{\frac{738 {800}}}
c A LaTex expression showing t = +\frac{\ln{738 times 800}}{0.02}
8
Rearrange this equation to solve for the time given this model of a continuous decay of a radioactive material?
A LaTex expression showing 347 =400 times e to the power of (-0.02 times t)
a A LaTex expression showing t = -0.02 over \ln{\frac{347 {400}}}
b A LaTex expression showing t = +\frac{\ln{347 times 400}}{0.02}
c A LaTex expression showing t = -\ln{\frac{347 over 400 }}{0.02}