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

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Exponential Function Solution Equation - Decay (Continuous, Mis-match...
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 830.
Rearrange the exponential equation to solve for for the starting population given this scenario?
a A LaTex expression showing P sub 0 = 830 over e to the power of (-0.04 times \frac{2 {4 )}}
b A LaTex expression showing P sub 0 = e to the power of (-0.04 times \frac{2 over 4 ) }{830}
c A LaTex expression showing P sub 0 = 830 over e to the power of (\frac{-0.04 {2 times 4 )}}
2
A radioactive material starts at a certain isotope concentration. It decays continuously at 3% per day. After 2 weeks it has decayed to an isotope concentration of 753ppm.
Rearrange the exponential equation to solve for for the starting concentration given this scenario?
a A LaTex expression showing R sub 0 = 753 over e to the power of (\frac{-0.03 {2 over 7 )}}
b A LaTex expression showing R sub 0 = 753 over e to the power of (-0.03 times 2 times 7)
3
A toxin starts at a certain concentration. It declines continuously at 6% per day. After 7 weeks it has decreased to a concentration of 525mg/L.
Rearrange the exponential equation to solve for for the starting concentration given this scenario?
a A LaTex expression showing C sub 0 = \frac{e to the power of (-0.06 times 7 times 7) }{525}
b A LaTex expression showing C sub 0 = 525 over e to the power of (-0.06 times 7 times 7)
c A LaTex expression showing C sub 0 = 525 over e to the power of (\frac{-0.06 {7 over 7 )}}
4
A whale population starts at a certain size. It declines continuously at 4% per quarter. After 7 years it has decreased to a population of 151 whales.
Rearrange the exponential equation to solve for for the starting population given this scenario?
a A LaTex expression showing P sub 0 = 151 over e to the power of (\frac{-0.04 {7 over 4 )}}
b A LaTex expression showing P sub 0 = \frac{e to the power of (-0.04 times 7 times 4) }{151}
c A LaTex expression showing P sub 0 = 151 over e to the power of (-0.04 times 7 times 4)
5
A bird population starts at a certain size. It declines continuously at 8% per year. After 5 quarters it has decreased to a population of 201.
Rearrange the exponential equation to solve for for the starting population given this scenario?
a A LaTex expression showing P sub 0 = e to the power of (-0.08 times \frac{5 over 4 ) }{201}
b A LaTex expression showing P sub 0 = 201 over e to the power of (-0.08 times \frac{5 {4 )}}
c A LaTex expression showing P sub 0 = 201 over e to the power of (\frac{-0.08 {5 times 4 )}}
6
A radioactive material starts at a certain isotope concentration. It decays continuously at 8% per day. After 6 hours it has decayed to an isotope concentration of 123ppm.
Rearrange the exponential equation to solve for for the starting concentration given this scenario?
a A LaTex expression showing R sub 0 = e to the power of (-0.08 times \frac{6 over 24 ) }{123}
b A LaTex expression showing R sub 0 = 123 over e to the power of (\frac{-0.08 {6 times 24 )}}
c A LaTex expression showing R sub 0 = 123 over e to the power of (-0.08 times \frac{6 {24 )}}
7
A bird population starts at a certain size. It declines continuously at 7% per year. After 9 quarters it has decreased to a population of 426.
Rearrange the exponential equation to solve for for the starting population given this scenario?
a A LaTex expression showing P sub 0 = e to the power of (-0.07 times \frac{9 over 4 ) }{426}
b A LaTex expression showing P sub 0 = 426 over e to the power of (-0.07 times \frac{9 {4 )}}
c A LaTex expression showing P sub 0 = 426 over e to the power of (\frac{-0.07 {9 times 4 )}}
8
A whale population starts at a certain size. It declines continuously at 7% per year. After 5 quarters it has decreased to a population of 211 whales.
Rearrange the exponential equation to solve for for the starting population given this scenario?
a A LaTex expression showing P sub 0 = 211 over e to the power of (-0.07 times \frac{5 {4 )}}
b A LaTex expression showing P sub 0 = 211 over e to the power of (\frac{-0.07 {5 times 4 )}}
c A LaTex expression showing P sub 0 = e to the power of (-0.07 times \frac{5 over 4 ) }{211}