Writing Exponential Growth/Decay Equations

Below, you can practice writing equations for word problems that represent various types of exponential growth.

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: \(A(t)=P(1 + r)^t\)
  • Simplify \((1 + r)\) and use a zero for values less than 1.
  • For example, (1 - 0.03)^t should be typed as (0.97)^t and not (.97)^t.
  
  
• Compound Growth: \(A(t)=P(1 + \frac{r}{n})^{nt}\)
  • DO NOT simplify the \((1+\frac{r}{n})\).
  • For example, \((1+\frac{0.13}{12})^{12t}\) should be typed as (1+0.13/12)^12t making sure to have a zero in front of the decimal.
  
  
• Continuous Growth: \(A(t)=Pe^{rt}\)