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

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 Rate Worksheet

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Exponential Function Solving - Decay (Continuous, Mis-matched Time Un...
1
A bird population starts at 400. It declines continuously at a certain percent per quarter. After 7 years it has decreased to a population of 347.
How would you solve for the rate given this scenario?
a A LaTex expression showing r = -e to the power of \frac{P over P sub 0 }{t times 4}
b A LaTex expression showing r = -\ln{\frac{P over P sub 0 }}{t times 4}
2
A whale population starts at 300. It declines continuously at a certain percent per year. After 9 quarters it has decreased to a population of 174 whales.
How would you solve for the rate given this scenario?
a A LaTex expression showing r = -\ln{\frac{P over P sub 0 }}{t over 4 }
b A LaTex expression showing r = -\ln{\frac{P sub 0 over P }}{t times 4}
c A LaTex expression showing r = -e to the power of \frac{P over P sub 0 }{t over 4 }
3
A bird population starts at 600. It declines continuously at a certain percent per quarter. After 4 years it has decreased to a population of 435.
How would you solve for the rate given this scenario?
a A LaTex expression showing r = -\ln{\frac{P over P sub 0 }}{t times 4}
b A LaTex expression showing r = -e to the power of \frac{P over P sub 0 }{t times 4}
4
A bacteria population starts at 700. It declines continuously at a certain percent per day. After 5 years it has decreased to a population of 469 bacteria.
How would you solve for the rate given this scenario?
a A LaTex expression showing r = -\ln{\frac{P over P sub 0 }}{t times 365}
b A LaTex expression showing r = -e to the power of \frac{P over P sub 0 }{t times 365}
c A LaTex expression showing r = -\ln{\frac{P sub 0 over P }}{t over 365 }
5
A radioactive material starts at an isotope concentration of 500ppm. It decays continuously at a certain percent per day. After 6 weeks it has decayed to an isotope concentration of 291ppm.
How would you solve for the rate of decay given this scenario?
a A LaTex expression showing r = -\ln{\frac{R over R sub 0 }}{t times 7}
b A LaTex expression showing r = -e to the power of \frac{R over R sub 0 }{t times 7}
c A LaTex expression showing r = -\ln{\frac{R sub 0 over R }}{t over 7 }
6
A bird population starts at 500. It declines continuously at a certain percent per quarter. After 4 years it has decreased to a population of 393.
How would you solve for the rate given this scenario?
a A LaTex expression showing r = -e to the power of \frac{P over P sub 0 }{t times 4}
b A LaTex expression showing r = -\ln{\frac{P over P sub 0 }}{t times 4}
c A LaTex expression showing r = -\ln{\frac{P sub 0 over P }}{t over 4 }
7
A bacteria population starts at 600. It declines continuously at a certain percent per year. After 7 months it has decreased to a population of 453 bacteria.
How would you solve for the rate given this scenario?
a A LaTex expression showing r = -\ln{\frac{P over P sub 0 }}{t over 12 }
b A LaTex expression showing r = -e to the power of \frac{P over P sub 0 }{t over 12 }
c A LaTex expression showing r = -\ln{\frac{P sub 0 over P }}{t times 12}
8
A bird population starts at 900. It declines continuously at a certain percent per year. After 4 quarters it has decreased to a population of 736.
How would you solve for the rate given this scenario?
a A LaTex expression showing r = -\ln{\frac{P sub 0 over P }}{t times 4}
b A LaTex expression showing r = -e to the power of \frac{P over P sub 0 }{t over 4 }
c A LaTex expression showing r = -\ln{\frac{P over P sub 0 }}{t over 4 }