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}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20A%28t%29%3D115%281.025%29%5Et%20%5C%5C%20B%28t%29%3D82%281.029%29%5Et%20%5Cend%7Bgathered%7D)
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](https://tex.z-dn.net/?f=A%2820%29%3D115%281.025%29%5E%7B20%7D%5Capprox188)
![B(20)=82(1.029)^{20}\approx145](https://tex.z-dn.net/?f=B%2820%29%3D82%281.029%29%5E%7B20%7D%5Capprox145)
Hence, forest A has a greater number of trees after 20 years.
Calculate the difference:
![188-145=43](https://tex.z-dn.net/?f=188-145%3D43)
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.