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.