Exponential Function Solution Equation - Decay (Continuous) Equation to Rate

Level 1

This math topic focuses on solving exponential decay problems in continuous systems by rearranging equations to find the decay rate (r). It involves practical scenarios such as the decline in wildlife populations and reductions in toxin concentrations. Students practice isolating the decay rate 'r' from given equations, sharpening their skills in manipulating exponential functions and logarithms. Each question presents an exponential function that models a decay process, and students must use logarithmic manipulation to solve for the decay rate. The problems are labeled as Level 1, suggesting they are introductory exercises in understanding exponential decay equations.

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 Rate Worksheet

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Exponential Function Solution Equation - Decay (Continuous) Equation ...
1
Rearrange this equation to solve for the rate given this model of a continuous decline of a whale population?
A LaTex expression showing 162 =200 times e to the power of (-r times 7)
a A LaTex expression showing r = -\ln{\frac{162 over 200 }}{7}
b A LaTex expression showing r = -e to the power of \frac{162 over 200 }{7}
c A LaTex expression showing r = -\ln{\frac{200 over 162 }}{7}
2
Rearrange this equation to solve for the rate given this model of a continuous reduction of a toxin concentration?
A LaTex expression showing 471 =600 times e to the power of (-r times 3)
a A LaTex expression showing r = -\ln{\frac{471 over 600 }}{3}
b A LaTex expression showing r = -\ln{\frac{600 over 471 }}{3}
3
Rearrange this equation to solve for the rate given this model of a continuous decline of a whale population?
A LaTex expression showing 361 =400 times e to the power of (-r times 5)
a A LaTex expression showing r = -\ln{\frac{400 over 361 }}{5}
b A LaTex expression showing r = -\ln{\frac{361 over 400 }}{5}
c A LaTex expression showing r = -e to the power of \frac{361 over 400 }{5}
4
Rearrange this equation to solve for the rate given this model of a continuous reduction of a toxin concentration?
A LaTex expression showing 680 =900 times e to the power of (-r times 4)
a A LaTex expression showing r = -\ln{\frac{900 over 680 }}{4}
b A LaTex expression showing r = -\ln{\frac{680 over 900 }}{4}
c A LaTex expression showing r = -e to the power of \frac{680 over 900 }{4}
5
Rearrange this equation to solve for the rate given this model of a continuous decline of a bird population?
A LaTex expression showing 157 =200 times e to the power of (-r times 8)
a A LaTex expression showing r = -\ln{\frac{200 over 157 }}{8}
b A LaTex expression showing r = -e to the power of \frac{157 over 200 }{8}
c A LaTex expression showing r = -\ln{\frac{157 over 200 }}{8}
6
Rearrange this equation to solve for the rate given this model of a continuous decline of a whale population?
A LaTex expression showing 334 =400 times e to the power of (-r times 9)
a A LaTex expression showing r = -\ln{\frac{334 over 400 }}{9}
b A LaTex expression showing r = -\ln{\frac{400 over 334 }}{9}
c A LaTex expression showing r = -e to the power of \frac{334 over 400 }{9}
7
Rearrange this equation to solve for the rate given this model of a continuous reduction of a toxin concentration?
A LaTex expression showing 461 =500 times e to the power of (-r times 2)
a A LaTex expression showing r = -\ln{\frac{500 over 461 }}{2}
b A LaTex expression showing r = -e to the power of \frac{461 over 500 }{2}
c A LaTex expression showing r = -\ln{\frac{461 over 500 }}{2}
8
Rearrange this equation to solve for the rate given this model of a continuous decline of a bird population?
A LaTex expression showing 707 =900 times e to the power of (-r times 4)
a A LaTex expression showing r = -\ln{\frac{900 over 707 }}{4}
b A LaTex expression showing r = -e to the power of \frac{707 over 900 }{4}
c A LaTex expression showing r = -\ln{\frac{707 over 900 }}{4}