Exponential Function Solving - Decay (Continuous) - Equation to Time

Level 1

This math topic covers solving exponential decay functions, specifically focusing on finding the time variable in continuous decay scenarios. It includes problems pertinent to various real-world models, like the decline in populations of birds, bacteria, radioactive materials, and whales. Each question provides an exponential decay equation related to a specific scenario and asks to solve for the time (t) required for the equation to hold true. The problems aim to enhance understanding of exponential functions in continuous decay contexts, employing logarithms and basic algebra to isolate and solve for t.

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 Time Worksheet

Exponential Function Solving - Decay (Continuous) - Equation to Time

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

A LaTex expression showing 185 =300 times e to the power of (-0.06 times t)

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

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

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

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

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

A LaTex expression showing 830 =900 times e to the power of (-0.04 times t)

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

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

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

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

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

A LaTex expression showing 426 =800 times e to the power of (-0.07 times t)

a $A LaTex expression showing 9 + t = -\frac{\ln{R times R sub 0 }}{r}$

b $A LaTex expression showing 4 + t = -\frac{\ln{R times R sub 0 }}{r}$

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

d $A LaTex expression showing 7 + t = -r over \ln{\frac{R {R sub 0 }}}$

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

A LaTex expression showing 501 =600 times e to the power of (-0.02 times t)

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

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

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

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

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

A LaTex expression showing 377 =500 times e to the power of (-0.04 times t)

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

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

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

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

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

A LaTex expression showing 668 =800 times e to the power of (-0.02 times t)

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

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

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

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

A LaTex expression showing 106 =200 times e to the power of (-0.09 times t)

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

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

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

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

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

A LaTex expression showing 466 =800 times e to the power of (-0.06 times t)

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

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

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