Solving Exponential Growth/Decay Equations

Below, you will be given a word problem situation representing exponential growth. Think of the equation that represents this growth and then solve using the given output. You may need to solve by graphing or use logs to solve.

Use the following equations, where

• \(A=\) the new amount
• \(P=\) the original amount
• \(r=\) the rate of growth as a decimal (not a percent)
• \(t=\) time of growth
• \(n=\) the number of times the growth is compounded over one period
• \(e=\) Euler's constant

EXPONENTIAL GROWTH FORMULAS

• General Growth: \(A(t)=P(1 + r)^t\)
• Compound Growth: \(A(t)=P(1 + \frac{r}{n})^{nt}\)
• Continuous Growth: \(A(t)=Pe^{rt}\)