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

Level 1

This math topic focuses on solving exponential growth equations to find the time variable in different scenarios. It explores discrete exponential function growth models applied to examples like rabbit and insect population growth, credit card debt, and compounded savings growth. Each problem presents a mathematical model where students must solve for time, using formulas involving logarithms and base growth rates. Scenarios are diverse, incorporating yearly breeding cycles, monthly and quarterly interest or compounding, enhancing the understanding and application of exponential functions in real-world contexts.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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

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

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

A LaTex expression showing 1,074 =900 times (1+0.03) to the power of (t)

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

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

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

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

Solve for the time given this model of a growth of an insect population that breeds once per year?

A LaTex expression showing 789 =600 times (1+0.04) to the power of (t)

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

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

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

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

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

A LaTex expression showing 735 =600 times (1+0.07) 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 $A LaTex expression showing 5 + t = \ln{\frac{P over P sub 0 }}{\ln{(1-r)}}$

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

Solve for the time given this model of a growth in credit card debt with quarterly interest?

A LaTex expression showing 1,070 =800 times (1+0.06) to the power of (t)

a $A LaTex expression showing 3 + t = \ln{\frac{D over D sub 0 }}{\ln{(1-r)}}$

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

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

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

Solve for the time given this model of a monthly compounding growth of money in a savings account?

A LaTex expression showing 684 =500 times (1+0.04) to the power of (t)

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

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

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

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

Solve for the time given this model of a quarterly compounding growth of money in a savings account?

A LaTex expression showing 848 =800 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 $A LaTex expression showing 6 + t = \ln{\frac{P over P sub 0 }}{\ln{(1-r)}}$

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

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

Solve for the time given this model of a growth in credit card debt with yearly interest?

A LaTex expression showing 735 =400 times (1+0.07) to the power of (t)

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

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

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

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

Solve for the time given this model of a monthly compounding growth of money in a savings account?

A LaTex expression showing 865 =800 times (1+0.04) to the power of (t)

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

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

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