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

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Exponential Function Solution Equation - Decay (Continuous, Mis-match...
1
A toxin starts at a concentration of 200mg/L. It declines continuously at 8% per week. After a certain number of days it has decreased to a concentration of 134mg/L.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = -7 times \ln{\frac{134 over 200 }}{0.08}
b A LaTex expression showing t = -7 times 0.08 over \ln{\frac{134 {200}}}
c A LaTex expression showing t = +1 over 7 times \frac{\ln{134 times 200}}{0.08}
2
A radioactive material starts at an isotope concentration of 900ppm. It decays continuously at 5% per day. After a certain number of weeks it has decayed to an isotope concentration of 736ppm.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = -7 times \ln{\frac{736 over 900 }}{0.05}
b A LaTex expression showing t = -1 over 7 times \ln{\frac{736 over 900 }}{0.05}
c A LaTex expression showing t = +7 times \frac{\ln{736 times 900}}{0.05}
3
A bird population starts at 600. It declines continuously at 2% per year. After a certain number of quarters it has decreased to a population of 511.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = -4 times 0.02 over \ln{\frac{511 {600}}}
b A LaTex expression showing t = -4 times \ln{\frac{511 over 600 }}{0.02}
4
A radioactive material starts at an isotope concentration of 600ppm. It decays continuously at 2% per week. After a certain number of days it has decayed to an isotope concentration of 501ppm.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = -7 times \ln{\frac{501 over 600 }}{0.02}
b A LaTex expression showing t = +1 over 7 times \frac{\ln{501 times 600}}{0.02}
5
A bacteria population starts at 600. It declines continuously at 5% per day. After a certain number of years it has decreased to a population of 542 bacteria.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = -1 over 365 times \ln{\frac{542 over 600 }}{0.05}
b A LaTex expression showing t = +365 times \frac{\ln{542 times 600}}{0.05}
c A LaTex expression showing t = -365 times \ln{\frac{542 over 600 }}{0.05}
6
A radioactive material starts at an isotope concentration of 200ppm. It decays continuously at 9% per day. After a certain number of hours it has decayed to an isotope concentration of 97ppm.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = +1 over 24 times \frac{\ln{97 times 200}}{0.09}
b A LaTex expression showing t = -24 times \ln{\frac{97 over 200 }}{0.09}
c A LaTex expression showing t = -24 times 0.09 over \ln{\frac{97 {200}}}
d A LaTex expression showing t = -1 over 24 times \ln{\frac{97 over 200 }}{0.09}
7
A toxin starts at a concentration of 600mg/L. It declines continuously at 8% per week. After a certain number of days it has decreased to a concentration of 511mg/L.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = -7 times \ln{\frac{511 over 600 }}{0.08}
b A LaTex expression showing t = -1 over 7 times \ln{\frac{511 over 600 }}{0.08}
c A LaTex expression showing t = -7 times 0.08 over \ln{\frac{511 {600}}}
8
A whale population starts at 500. It declines continuously at 9% per quarter. After a certain number of years it has decreased to a population of 266 whales.
Rearrange the exponential equation to solve for for the time given this scenario?
a A LaTex expression showing t = -4 times \ln{\frac{266 over 500 }}{0.09}
b A LaTex expression showing t = -1 over 4 times 0.09 over \ln{\frac{266 {500}}}
c A LaTex expression showing t = -1 over 4 times \ln{\frac{266 over 500 }}{0.09}