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

Level 1

This math topic focuses on solving for time in exponential decay functions, using equations of the form \(P = P_0 \times (1 - r)^t\), where \(P\) represents the final population or amount, \(P_0\) is the initial population or amount, \(r\) is the rate of decay, and \(t\) is the time. Problems include scenarios involving declines in bird and whale populations, the balance of a charitable endowment with monthly disbursements, and the decline in toxin concentrations with dialysis treatments. Students are provided equations and asked to solve for the variable \(t\) to determine the time it would take to reach a given status.

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Exponential Function Solving - Decay (Discrete) - Equation to Time Worksheet

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

Solve for the time given this model of a decline of a bird population (yearly breeding cycle)?

A LaTex expression showing 752 =800 times (1-0.02) to the power of (t)

a $A LaTex expression showing 5 + t = \ln{\frac{P over P sub 0 }}{\ln{(1+r)}}$

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

c $A LaTex expression showing 2 + t = \frac{\ln{P times P sub 0 }}{\ln{(1-r)}}$

Solve for the time given this model of a decline of a bird population (yearly breeding cycle)?

A LaTex expression showing 456 =600 times (1-0.03) to the power of (t)

a $A LaTex expression showing t = \ln{\frac{P over P sub 0 }}{\ln{(1-r)}}$

b $A LaTex expression showing 5 + t = \ln{\frac{P over P sub 0 }}{\ln{(1+r)}}$

c $A LaTex expression showing 5 + t = \frac{\ln{P times P sub 0 }}{\ln{(1-r)}}$

d $A LaTex expression showing 2 + t = \frac{\ln{P times P sub 0 }}{\ln{(1-r)}}$

Solve for the time given this model of a decline of a whale population (yearly breeding cycle)?

A LaTex expression showing 673 =900 times (1-0.07) to the power of (t)

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

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

c $A LaTex expression showing 3 + t = \frac{\ln{P times P sub 0 }}{\ln{(1-r)}}$

d $A LaTex expression showing t = \ln{\frac{P over P sub 0 }}{\ln{(1-r)}}$

Solve for the time given this model of a decline of a bird population (yearly breeding cycle)?

A LaTex expression showing 652 =800 times (1-0.04) to the power of (t)

a $A LaTex expression showing 4 + t = \ln{\frac{P over P sub 0 }}{\ln{(1+r)}}$

b $A LaTex expression showing 6 + t = \ln{\frac{P over P sub 0 }}{\ln{(1+r)}}$

c $A LaTex expression showing t = \ln{\frac{P over P sub 0 }}{\ln{(1-r)}}$

d $A LaTex expression showing 6 + t = \frac{\ln{P times P sub 0 }}{\ln{(1-r)}}$

Solve for the time given this model of a balance of a charitable endowment (monthly disbursements)?

A LaTex expression showing 552 =600 times (1-0.04) to the power of (t)

a $A LaTex expression showing 6 + t = \frac{\ln{P times P sub 0 }}{\ln{(1-r)}}$

b $A LaTex expression showing 8 + t = \ln{\frac{P over P sub 0 }}{\ln{(1+r)}}$

c $A LaTex expression showing t = \ln{\frac{P over P sub 0 }}{\ln{(1-r)}}$

d $A LaTex expression showing 4 + t = \ln{\frac{P over P sub 0 }}{\ln{(1+r)}}$

Solve for the time given this model of a decline of a toxin concentration (monthly dialysis)?

A LaTex expression showing 515 =600 times (1-0.03) to the power of (t)

a $A LaTex expression showing 1 + t = \frac{\ln{C times C sub 0 }}{\ln{(1-r)}}$

b $A LaTex expression showing 2 + t = \ln{\frac{C over C sub 0 }}{\ln{(1+r)}}$

c $A LaTex expression showing 5 + t = \ln{\frac{C over C sub 0 }}{\ln{(1+r)}}$

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

Solve for the time given this model of a decline of a toxin concentration (hourly dialysis)?

A LaTex expression showing 163 =200 times (1-0.04) to the power of (t)

a $A LaTex expression showing 7 + t = \ln{\frac{C over C sub 0 }}{\ln{(1+r)}}$

b $A LaTex expression showing 9 + t = \frac{\ln{C times C sub 0 }}{\ln{(1-r)}}$

c $A LaTex expression showing t = \ln{\frac{C over C sub 0 }}{\ln{(1-r)}}$

d $A LaTex expression showing 8 + t = \frac{\ln{C times C sub 0 }}{\ln{(1-r)}}$

Solve for the time given this model of a decline of a bird population (yearly breeding cycle)?

A LaTex expression showing 579 =700 times (1-0.09) to the power of (t)

a $A LaTex expression showing t = \ln{\frac{P over P sub 0 }}{\ln{(1-r)}}$

b $A LaTex expression showing 9 + t = \ln{\frac{P over P sub 0 }}{\ln{(1+r)}}$

c $A LaTex expression showing 7 + t = \frac{\ln{P times P sub 0 }}{\ln{(1-r)}}$

d $A LaTex expression showing 4 + t = \ln{\frac{P over P sub 0 }}{\ln{(1+r)}}$