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

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Exponential Function Solution Equation - Decay (Continuous, Mis-match...
1
A bacteria population starts at 400. It declines continuously at a certain percent per year. After 3 months it has decreased to a population of 314 bacteria.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = -\ln{\frac{400 over 314 }}{3 times 12}
b A LaTex expression showing r = -e to the power of \frac{314 over 400 }{3 over 12 }
c A LaTex expression showing r = -\ln{\frac{314 over 400 }}{3 over 12 }
2
A radioactive material starts at an isotope concentration of 800ppm. It decays continuously at a certain percent per day. After 6 weeks it has decayed to an isotope concentration of 709ppm.
Rearrange the exponential equation to solve for for the rate of decay given this scenario?
a A LaTex expression showing r = -\ln{\frac{800 over 709 }}{6 over 7 }
b A LaTex expression showing r = -e to the power of \frac{709 over 800 }{6 times 7}
c A LaTex expression showing r = -\ln{\frac{709 over 800 }}{6 times 7}
3
A whale population starts at 400. It declines continuously at a certain percent per quarter. After 2 years it has decreased to a population of 376 whales.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = -\ln{\frac{376 over 400 }}{2 times 4}
b A LaTex expression showing r = -\ln{\frac{400 over 376 }}{2 over 4 }
c A LaTex expression showing r = -e to the power of \frac{376 over 400 }{2 times 4}
4
A radioactive material starts at an isotope concentration of 800ppm. It decays continuously at a certain percent per hour. After 9 days it has decayed to an isotope concentration of 668ppm.
Rearrange the exponential equation to solve for for the rate of decay given this scenario?
a A LaTex expression showing r = -e to the power of \frac{668 over 800 }{9 times 24}
b A LaTex expression showing r = -\ln{\frac{668 over 800 }}{9 times 24}
c A LaTex expression showing r = -\ln{\frac{800 over 668 }}{9 over 24 }
5
A bacteria population starts at 700. It declines continuously at a certain percent per year. After 4 months it has decreased to a population of 508 bacteria.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = -\ln{\frac{508 over 700 }}{4 over 12 }
b A LaTex expression showing r = -\ln{\frac{700 over 508 }}{4 times 12}
c A LaTex expression showing r = -e to the power of \frac{508 over 700 }{4 over 12 }
6
A radioactive material starts at an isotope concentration of 600ppm. It decays continuously at a certain percent per day. After 5 hours it has decayed to an isotope concentration of 402ppm.
Rearrange the exponential equation to solve for for the rate of decay given this scenario?
a A LaTex expression showing r = -\ln{\frac{600 over 402 }}{5 times 24}
b A LaTex expression showing r = -e to the power of \frac{402 over 600 }{5 over 24 }
c A LaTex expression showing r = -\ln{\frac{402 over 600 }}{5 over 24 }
7
A bird population starts at 900. It declines continuously at a certain percent per year. After 5 quarters it has decreased to a population of 774.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = -\ln{\frac{774 over 900 }}{5 over 4 }
b A LaTex expression showing r = -\ln{\frac{900 over 774 }}{5 times 4}
8
A bird population starts at 800. It declines continuously at a certain percent per quarter. After 2 years it has decreased to a population of 753.
Rearrange the exponential equation to solve for for the rate given this scenario?
a A LaTex expression showing r = -\ln{\frac{800 over 753 }}{2 over 4 }
b A LaTex expression showing r = -\ln{\frac{753 over 800 }}{2 times 4}
c A LaTex expression showing r = -e to the power of \frac{753 over 800 }{2 times 4}