Question

The population o f Charlestown was about 32,000 in 2013 , and the exponential growth rate was 1.2% per year. Write an exponential function describing the population ofCharlestown.

Answer 1

The initial population in 2013 is given to be 32,000

The exponential function can be derived as follows

`P=P_0((100+r)/(100))^n`

where

`\begin{gathered} P_0=\text{initial population} \\ r=\text{rate of growth} \\ n=n\\u\text{mber of years} \end{gathered}`

In our case

`\begin{gathered} P_0=32,000 \\ r=1.2 \\ n=n \end{gathered}`

Upon substituting

`P=32000((100+1.2)/(100))^n`

This is simplified to give

`P=32000(1.012)^n`