Question

In 1970, the population of a small town was 4,200. The population is decreasing at a rate of 2.4% per year. How can you write an exponential decay function to find the quarterly decay rate?

Answer 1

`\begin{gathered} \text{exponential decay} \\ y=a(1-r)^x \\ \text{where} \\ a=initial\text{ value} \\ r=decay\text{ rate (expressed as decimal)} \\ x=\text{the number of times inveterval that have passed} \end{gathered}`
`\begin{gathered} In\text{ our case} \\ a=4200 \\ r=0.024 \\ \text{hence,} \\ y=4200(0.024)^x \end{gathered}`