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

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Exponential Function Solving - Decay (Continuous, Mis-matched Time Un...
1
A radioactive material starts at an isotope concentration of 200ppm. It decays continuously at 3% per hour. After a certain number of days it has decayed to an isotope concentration of 152ppm.
How would you solve for the time given this scenario?
a A LaTex expression showing t = -1 over 24 times r over \ln{\frac{R {R sub 0 }}}
b A LaTex expression showing t = -1 over 24 times \ln{\frac{R over R sub 0 }}{r}
c A LaTex expression showing t = -24 times \ln{\frac{R over R sub 0 }}{r}
d A LaTex expression showing t = -24 times \frac{\ln{R times R sub 0 }}{r}
2
A bird population starts at 600. It declines continuously at 4% per year. After a certain number of quarters it has decreased to a population of 491.
How would you solve for the time given this scenario?
a A LaTex expression showing t = -4 times \ln{\frac{P over P sub 0 }}{r}
b A LaTex expression showing t = -4 times r over \ln{\frac{P {P sub 0 }}}
c A LaTex expression showing t = -1 over 4 times \ln{\frac{P over P sub 0 }}{r}
3
A bird population starts at 200. It declines continuously at 3% per quarter. After a certain number of years it has decreased to a population of 152.
How would you solve for the time given this scenario?
a A LaTex expression showing t = -1 over 4 times r over \ln{\frac{P {P sub 0 }}}
b A LaTex expression showing t = -1 over 4 times \ln{\frac{P over P sub 0 }}{r}
c A LaTex expression showing t = -4 times \frac{\ln{P times P sub 0 }}{r}
4
A bird population starts at 400. It declines continuously at 3% per quarter. After a certain number of years it has decreased to a population of 324.
How would you solve for the time given this scenario?
a A LaTex expression showing t = -4 times \frac{\ln{P times P sub 0 }}{r}
b A LaTex expression showing t = -4 times \ln{\frac{P over P sub 0 }}{r}
c A LaTex expression showing t = -1 over 4 times \ln{\frac{P over P sub 0 }}{r}
d A LaTex expression showing t = -1 over 4 times r over \ln{\frac{P {P sub 0 }}}
5
A radioactive material starts at an isotope concentration of 400ppm. It decays continuously at 2% per week. After a certain number of days it has decayed to an isotope concentration of 340ppm.
How would you solve for the time given this scenario?
a A LaTex expression showing t = -7 times \ln{\frac{R over R sub 0 }}{r}
b A LaTex expression showing t = -1 over 7 times \ln{\frac{R over R sub 0 }}{r}
c A LaTex expression showing t = -7 times r over \ln{\frac{R {R sub 0 }}}
6
A radioactive material starts at an isotope concentration of 700ppm. It decays continuously at 3% per day. After a certain number of weeks it has decayed to an isotope concentration of 602ppm.
How would you solve for the time given this scenario?
a A LaTex expression showing t = -7 times \ln{\frac{R over R sub 0 }}{r}
b A LaTex expression showing t = -7 times \frac{\ln{R times R sub 0 }}{r}
c A LaTex expression showing t = -1 over 7 times \ln{\frac{R over R sub 0 }}{r}
7
A whale population starts at 200. It declines continuously at 6% per quarter. After a certain number of years it has decreased to a population of 131 whales.
How would you solve for the time given this scenario?
a A LaTex expression showing t = -4 times \ln{\frac{P over P sub 0 }}{r}
b A LaTex expression showing t = -1 over 4 times r over \ln{\frac{P {P sub 0 }}}
c A LaTex expression showing t = -1 over 4 times \ln{\frac{P over P sub 0 }}{r}
8
A radioactive material starts at an isotope concentration of 500ppm. It decays continuously at 8% per day. After a certain number of weeks it has decayed to an isotope concentration of 285ppm.
How would you solve for the time given this scenario?
a A LaTex expression showing t = -1 over 7 times \ln{\frac{R over R sub 0 }}{r}
b A LaTex expression showing t = -7 times \frac{\ln{R times R sub 0 }}{r}
c A LaTex expression showing t = -1 over 7 times r over \ln{\frac{R {R sub 0 }}}
d A LaTex expression showing t = -7 times \ln{\frac{R over R sub 0 }}{r}