Exponential Function Solving - Decay (Continuous) Equation to Rate

Level 1

This math topic involves practicing the solving of exponential decay problems in continuous scenarios. Specifically, learners are tasked with finding the decay rate from various models of declining populations or concentrations. These problems use the mathematical representation of decay processes, where the formula given generally includes a natural exponential function with a decay factor. Each question is multiple-choice, requiring the selection of the correct formulation that relates initial conditions, time, and the variable decay rate. This topic is an introduction to understanding and applying exponential functions to real-world decay situations.

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 Rate Worksheet

Exponential Function Solving - Decay (Continuous) Equation to Rate

Solve for the rate given this model of a continuous decline of a whale population?

A LaTex expression showing 226 =300 times e to the power of (-r times 7)

a $A LaTex expression showing 0 + r = -\ln{\frac{P sub 0 over P }}{t}$

b $A LaTex expression showing 1 + r = -\ln{\frac{P sub 0 over P }}{t}$

c $A LaTex expression showing r = -\ln{\frac{P over P sub 0 }}{t}$

d $A LaTex expression showing 3 + r = -\ln{\frac{P sub 0 over P }}{t}$

Solve for the rate given this model of a continuous reduction of a toxin concentration?

A LaTex expression showing 736 =900 times e to the power of (-r times 4)

a $A LaTex expression showing 9 + r = -e to the power of \frac{C over C sub 0 }{t}$

b $A LaTex expression showing r = -\ln{\frac{C over C sub 0 }}{t}$

c $A LaTex expression showing 3 + r = -\ln{\frac{C sub 0 over C }}{t}$

d $A LaTex expression showing 8 + r = -e to the power of \frac{C over C sub 0 }{t}$

Solve for the rate of decay given this model of a continuous decay of a radioactive material?

A LaTex expression showing 584 =700 times e to the power of (-r times 2)

a $A LaTex expression showing r = -\ln{\frac{R over R sub 0 }}{t}$

b $A LaTex expression showing 8 + r = -e to the power of \frac{R over R sub 0 }{t}$

c $A LaTex expression showing 0 + r = -e to the power of \frac{R over R sub 0 }{t}$

d $A LaTex expression showing 1 + r = -e to the power of \frac{R over R sub 0 }{t}$

Solve for the rate given this model of a continuous decline of a bird population?

A LaTex expression showing 511 =600 times e to the power of (-r times 8)

a $A LaTex expression showing 5 + r = -\ln{\frac{P sub 0 over P }}{t}$

b $A LaTex expression showing r = -\ln{\frac{P over P sub 0 }}{t}$

Solve for the rate given this model of a a continuously declining bacteria population?

A LaTex expression showing 610 =800 times e to the power of (-r times 9)

a $A LaTex expression showing 6 + r = -\ln{\frac{P sub 0 over P }}{t}$

b $A LaTex expression showing 2 + r = -\ln{\frac{P sub 0 over P }}{t}$

c $A LaTex expression showing r = -\ln{\frac{P over P sub 0 }}{t}$

d $A LaTex expression showing 7 + r = -e to the power of \frac{P over P sub 0 }{t}$

Solve for the rate given this model of a a continuously declining bacteria population?

A LaTex expression showing 201 =300 times e to the power of (-r times 5)

a $A LaTex expression showing 1 + r = -e to the power of \frac{P over P sub 0 }{t}$

b $A LaTex expression showing 9 + r = -e to the power of \frac{P over P sub 0 }{t}$

c $A LaTex expression showing 6 + r = -\ln{\frac{P sub 0 over P }}{t}$

d $A LaTex expression showing r = -\ln{\frac{P over P sub 0 }}{t}$

Solve for the rate given this model of a continuous decline of a whale population?

A LaTex expression showing 167 =200 times e to the power of (-r times 3)

a $A LaTex expression showing 4 + r = -\ln{\frac{P sub 0 over P }}{t}$

b $A LaTex expression showing 8 + r = -\ln{\frac{P sub 0 over P }}{t}$

c $A LaTex expression showing r = -\ln{\frac{P over P sub 0 }}{t}$

d $A LaTex expression showing 5 + r = -e to the power of \frac{P over P sub 0 }{t}$

Solve for the rate given this model of a continuous reduction of a toxin concentration?

A LaTex expression showing 145 =200 times e to the power of (-r times 8)

a $A LaTex expression showing 9 + r = -e to the power of \frac{C over C sub 0 }{t}$

b $A LaTex expression showing r = -\ln{\frac{C over C sub 0 }}{t}$

c $A LaTex expression showing 0 + r = -\ln{\frac{C sub 0 over C }}{t}$

d $A LaTex expression showing 1 + r = -\ln{\frac{C sub 0 over C }}{t}$