Question

A population numbers 513 organisms initially and increases by 3.6% each year.Suppose P represents population, and n the number of years of growth. Write an exponential model torepresent this situation.P=

Answer 1

`P=513(1.036)^n`

Explanation:

For a population growing exponentially with a rate of r%, the formula for the new population, P(n), after n years is:

`\begin{gathered} P(n)=P_o(1+r)^n \\ P_o=\text{Initial Population} \end{gathered}`

Given:

• Initial Population, Po = 513

,

• Rate = 3.6% = 0.036

Therefore, an exponential model to represent this situation is:

`\begin{gathered} P=513(1+0.036)^n \\ P=513(1.036)^n \end{gathered}`

The model is:

`P=513(1.036)^n`

.