Question

Assuming the population growth models continue to represent the growth of the forests, which forest will have a greater number of trees after 20 years? By how many?

Answer 1

The given population models for the trees is given as:

`\begin{gathered} A(t)=115(1.025)^t \\ B(t)=82(1.029)^t \end{gathered}`

It is required to find which forest will have a greater number of trees after 20 years and by how many.

To do this substitute t=20 in the equations of the models:

`A(20)=115(1.025)^(20)\approx188`
`B(20)=82(1.029)^(20)\approx145`

Hence, forest A has a greater number of trees after 20 years.

Calculate the difference:

`188-145=43`

It follows that forest A has a greater number of trees than forest B by 43 trees.

After 20 years, forest A has a greater number of trees than forest B by 43 trees.