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

Level 1

This math topic focuses on solving exponential decay equations to find the starting value, specifically for continuously declining populations. The problems involve rearranging exponential equations that model declines in different populations, such as whales, birds, and bacteria, to solve for the initial population size (denoted P₀). The exercises require understanding the exponential function, manipulating algebraic expressions, and applying logarithmic principles to isolate and solve for variables. This serves as an introductory exploration into handling real-world scenarios using mathematical modeling in exponential 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) Equation to Starting Value Worksheet

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Exponential Function Solution Equation - Decay (Continuous) Equation ...
1
Rearrange this equation to solve for the starting population given this model of a continuous decline of a whale population?
A LaTex expression showing 847 =P sub 0 times e to the power of (-0.02 times 3)
a A LaTex expression showing P sub 0 = 847 over e to the power of (\frac{-0.02 {3 )}}
b A LaTex expression showing P sub 0 = 847 over e to the power of (-0.02 times 3)
2
Rearrange this equation to solve for the starting population given this model of a continuous decline of a bird population?
A LaTex expression showing 247 =P sub 0 times e to the power of (-0.06 times 8)
a A LaTex expression showing P sub 0 = \frac{e to the power of (-0.06 times 8) }{247}
b A LaTex expression showing P sub 0 = 247 over e to the power of (\frac{-0.06 {8 )}}
c A LaTex expression showing P sub 0 = 247 over e to the power of (-0.06 times 8)
3
Rearrange this equation to solve for the starting population given this model of a a continuously declining bacteria population?
A LaTex expression showing 558 =P sub 0 times e to the power of (-0.04 times 9)
a A LaTex expression showing P sub 0 = \frac{e to the power of (-0.04 times 9) }{558}
b A LaTex expression showing P sub 0 = 558 over e to the power of (\frac{-0.04 {9 )}}
c A LaTex expression showing P sub 0 = 558 over e to the power of (-0.04 times 9)
4
Rearrange this equation to solve for the starting population given this model of a continuous decline of a whale population?
A LaTex expression showing 407 =P sub 0 times e to the power of (-0.06 times 9)
a A LaTex expression showing P sub 0 = 407 over e to the power of (\frac{-0.06 {9 )}}
b A LaTex expression showing P sub 0 = 407 over e to the power of (-0.06 times 9)
5
Rearrange this equation to solve for the starting population given this model of a a continuously declining bacteria population?
A LaTex expression showing 511 =P sub 0 times e to the power of (-0.02 times 8)
a A LaTex expression showing P sub 0 = 511 over e to the power of (-0.02 times 8)
b A LaTex expression showing P sub 0 = \frac{e to the power of (-0.02 times 8) }{511}
c A LaTex expression showing P sub 0 = 511 over e to the power of (\frac{-0.02 {8 )}}
6
Rearrange this equation to solve for the starting population given this model of a a continuously declining bacteria population?
A LaTex expression showing 668 =P sub 0 times e to the power of (-0.02 times 9)
a A LaTex expression showing P sub 0 = 668 over e to the power of (\frac{-0.02 {9 )}}
b A LaTex expression showing P sub 0 = 668 over e to the power of (-0.02 times 9)
7
Rearrange this equation to solve for the starting population given this model of a a continuously declining bacteria population?
A LaTex expression showing 243 =P sub 0 times e to the power of (-0.09 times 8)
a A LaTex expression showing P sub 0 = 243 over e to the power of (-0.09 times 8)
b A LaTex expression showing P sub 0 = 243 over e to the power of (\frac{-0.09 {8 )}}
c A LaTex expression showing P sub 0 = \frac{e to the power of (-0.09 times 8) }{243}
8
Rearrange this equation to solve for the starting concentration given this model of a continuous reduction of a toxin concentration?
A LaTex expression showing 532 =C sub 0 times e to the power of (-0.04 times 3)
a A LaTex expression showing C sub 0 = \frac{e to the power of (-0.04 times 3) }{532}
b A LaTex expression showing C sub 0 = 532 over e to the power of (\frac{-0.04 {3 )}}
c A LaTex expression showing C sub 0 = 532 over e to the power of (-0.04 times 3)