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Exponential Function Solving - Decay (Continuous) Equation to Starting Value

Level 1

This math topic focuses on solving exponential decay equations to find initial values, specifically within contexts like radioactive decay, population decline, and toxin reduction. Skills practiced include manipulating and rearranging exponential functions, understanding decay constants and initial conditions, and applying these concepts to various real-world scenarios. Each problem provides a decay model with specific parameters and asks to solve for the starting value or concentration, given certain conditions.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Exponential Function Solving - Decay (Continuous) Equation to Starting Value Worksheet

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Exponential Function Solving - Decay (Continuous) Equation to Startin...
1
Solve for the starting concentration given this model of a continuous decay of a radioactive material?
A LaTex expression showing 830 =R sub 0 times e to the power of (-0.02 times 4)
a A LaTex expression showing R sub 0 = R over e to the power of (-r times t)
b A LaTex expression showing 0 + R sub 0 = R over e to the power of (\frac{-r {t )}}
c A LaTex expression showing 2 + R sub 0 = \frac{e to the power of (-r times t) }{R}
d A LaTex expression showing 4 + R sub 0 = \frac{e to the power of (-r times t) }{R}
2
Solve for the starting concentration given this model of a continuous decay of a radioactive material?
A LaTex expression showing 534 =R sub 0 times e to the power of (-0.03 times 9)
a A LaTex expression showing 0 + R sub 0 = \frac{e to the power of (-r times t) }{R}
b A LaTex expression showing 9 + R sub 0 = R over e to the power of (\frac{-r {t )}}
c A LaTex expression showing 2 + R sub 0 = R over e to the power of (\frac{-r {t )}}
d A LaTex expression showing R sub 0 = R over e to the power of (-r times t)
3
Solve for the starting population given this model of a continuous decline of a whale population?
A LaTex expression showing 466 =P sub 0 times e to the power of (-0.09 times 6)
a A LaTex expression showing 0 + P sub 0 = \frac{e to the power of (-r times t) }{P}
b A LaTex expression showing 9 + P sub 0 = \frac{e to the power of (-r times t) }{P}
c A LaTex expression showing P sub 0 = P over e to the power of (-r times t)
d A LaTex expression showing 2 + P sub 0 = \frac{e to the power of (-r times t) }{P}
4
Solve for the starting population given this model of a a continuously declining bacteria population?
A LaTex expression showing 347 =P sub 0 times e to the power of (-0.02 times 7)
a A LaTex expression showing P sub 0 = P over e to the power of (-r times t)
b A LaTex expression showing 8 + P sub 0 = \frac{e to the power of (-r times t) }{P}
c A LaTex expression showing 6 + P sub 0 = \frac{e to the power of (-r times t) }{P}
d A LaTex expression showing 4 + P sub 0 = \frac{e to the power of (-r times t) }{P}
5
Solve for the starting population given this model of a a continuously declining bacteria population?
A LaTex expression showing 213 =P sub 0 times e to the power of (-0.09 times 7)
a A LaTex expression showing 4 + P sub 0 = P over e to the power of (\frac{-r {t )}}
b A LaTex expression showing 3 + P sub 0 = P over e to the power of (\frac{-r {t )}}
c A LaTex expression showing P sub 0 = P over e to the power of (-r times t)
d A LaTex expression showing 6 + P sub 0 = P over e to the power of (\frac{-r {t )}}
6
Solve for the starting concentration given this model of a continuous decay of a radioactive material?
A LaTex expression showing 140 =R sub 0 times e to the power of (-0.05 times 7)
a A LaTex expression showing 4 + R sub 0 = R over e to the power of (\frac{-r {t )}}
b A LaTex expression showing R sub 0 = R over e to the power of (-r times t)
c A LaTex expression showing 3 + R sub 0 = \frac{e to the power of (-r times t) }{R}
d A LaTex expression showing 2 + R sub 0 = R over e to the power of (\frac{-r {t )}}
7
Solve for the starting concentration given this model of a continuous reduction of a toxin concentration?
A LaTex expression showing 458 =C sub 0 times e to the power of (-0.03 times 9)
a A LaTex expression showing 0 + C sub 0 = C over e to the power of (\frac{-r {t )}}
b A LaTex expression showing 1 + C sub 0 = \frac{e to the power of (-r times t) }{C}
c A LaTex expression showing C sub 0 = C over e to the power of (-r times t)
d A LaTex expression showing 6 + C sub 0 = C over e to the power of (\frac{-r {t )}}
8
Solve for the starting concentration given this model of a continuous reduction of a toxin concentration?
A LaTex expression showing 521 =C sub 0 times e to the power of (-0.02 times 7)
a A LaTex expression showing C sub 0 = C over e to the power of (-r times t)
b A LaTex expression showing 0 + C sub 0 = \frac{e to the power of (-r times t) }{C}
c A LaTex expression showing 6 + C sub 0 = C over e to the power of (\frac{-r {t )}}
d A LaTex expression showing 3 + C sub 0 = \frac{e to the power of (-r times t) }{C}