Question

A population numbers 208 organisms initially and increases by 4.3% each year.Suppose P represents population, and n the number of years of growth. Write an exponential model torepresent this situation.P =

Answer 1

Recall the exponential growth model.

$\begin{gathered} y=a(1+r)^n \\ \text{where} \\ a\text{ is the initial number of population} \\ r\text{ is the rate of growth} \\ n\text{ is the time interval} \end{gathered}$

Using the given, we get

$\begin{gathered} r=4.3\%=0.043 \\ a=208 \\ y=P \\ \\ y=a(1+r)^n \\ P=208(1+0.043)^n \\ \\ \text{Therefore, the exponential model to reprsent this situation is} \\ P=208(1.043)^n \end{gathered}$