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

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 Starting Value Worksheet

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Exponential Function Solving - Decay (Continuous, Mis-matched Time Un...
1
A bird population starts at a certain size. It declines continuously at 4% per year. After 2 quarters it has decreased to a population of 461.
How would you solve for the starting population given this scenario?
a A LaTex expression showing P sub 0 = P over e to the power of (-r times \frac{t {4 )}}
b A LaTex expression showing P sub 0 = P over e to the power of (\frac{-r {t times 4 )}}
c A LaTex expression showing P sub 0 = e to the power of (-r times \frac{t over 4 ) }{P}
2
A toxin starts at a certain concentration. It declines continuously at 2% per week. After 8 days it has decreased to a concentration of 596mg/L.
How would you solve for the starting concentration given this scenario?
a A LaTex expression showing C sub 0 = e to the power of (-r times \frac{t over 7 ) }{C}
b A LaTex expression showing C sub 0 = C over e to the power of (\frac{-r {t times 7 )}}
c A LaTex expression showing C sub 0 = C over e to the power of (-r times \frac{t {7 )}}
3
A radioactive material starts at a certain isotope concentration. It decays continuously at 3% per hour. After 8 days it has decayed to an isotope concentration of 550ppm.
How would you solve for the starting concentration given this scenario?
a A LaTex expression showing R sub 0 = R over e to the power of (-r times t times 24)
b A LaTex expression showing R sub 0 = R over e to the power of (\frac{-r {t over 24 )}}
c A LaTex expression showing R sub 0 = \frac{e to the power of (-r times t times 24) }{R}
4
A bird population starts at a certain size. It declines continuously at 6% per quarter. After 8 years it has decreased to a population of 309.
How would you solve for the starting population given this scenario?
a A LaTex expression showing P sub 0 = \frac{e to the power of (-r times t times 4) }{P}
b A LaTex expression showing P sub 0 = P over e to the power of (\frac{-r {t over 4 )}}
c A LaTex expression showing P sub 0 = P over e to the power of (-r times t times 4)
5
A whale population starts at a certain size. It declines continuously at 7% per year. After 4 quarters it has decreased to a population of 680 whales.
How would you solve for the starting population given this scenario?
a A LaTex expression showing P sub 0 = P over e to the power of (-r times \frac{t {4 )}}
b A LaTex expression showing P sub 0 = P over e to the power of (\frac{-r {t times 4 )}}
6
A bird population starts at a certain size. It declines continuously at 6% per year. After 2 quarters it has decreased to a population of 798.
How would you solve for the starting population given this scenario?
a A LaTex expression showing P sub 0 = P over e to the power of (\frac{-r {t times 4 )}}
b A LaTex expression showing P sub 0 = e to the power of (-r times \frac{t over 4 ) }{P}
c A LaTex expression showing P sub 0 = P over e to the power of (-r times \frac{t {4 )}}
7
A whale population starts at a certain size. It declines continuously at 2% per year. After 4 quarters it has decreased to a population of 830 whales.
How would you solve for the starting population given this scenario?
a A LaTex expression showing P sub 0 = e to the power of (-r times \frac{t over 4 ) }{P}
b A LaTex expression showing P sub 0 = P over e to the power of (-r times \frac{t {4 )}}
8
A bacteria population starts at a certain size. It declines continuously at 7% per day. After 6 weeks it has decreased to a population of 197 bacteria.
How would you solve for the starting population given this scenario?
a A LaTex expression showing P sub 0 = \frac{e to the power of (-r times t times 7) }{P}
b A LaTex expression showing P sub 0 = P over e to the power of (\frac{-r {t over 7 )}}
c A LaTex expression showing P sub 0 = P over e to the power of (-r times t times 7)