For each year t, the population of a forest of trees is represented by the function A(t)= 115(1.025)^t. In a neighboring forest, the population of the same type of tree is represented by the function B(t)=82(1.029)^t. Assuming the population growth models continue to represent the growth of the forests, which forest will have a greater number of trees after 100 years? By how many?

Answer:71 treesStep-by-step explanation:Both populations are represented by the following equations:Forest A : A(t)= 115(1.025)^tForest B : B(t)=82(1.029)^tafter 100 years, ie t = 100, A(100)= 115(1.025)^100 = 1358.58andB(100)=82(1.029)^100 = 1430.05Comparing A(100) and B(100) we can see that forest B has the greater number of trees.DIfference in trees after 100 years= B(100) - A(100) = 1430.05 - 1358.58 = 71.47 treessince we cannot have a fraction of a tree (i.e 0.47 of a tree), we have to round down to get the lower number of whole trees of 71 trees