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?

Question

Mathematics

Gavyn Gentry

11 November, 03:54

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?

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Gilberto Woods · Answer 1

71 trees

Step-by-step explanation:

Both populations are represented by the following equations:

Forest A : A (t) = 115 (1.025) ^t

Forest B : B (t) = 82 (1.029) ^t

after 100 years, ie t = 100,

A (100) = 115 (1.025) ^100 = 1358.58

and

B (100) = 82 (1.029) ^100 = 1430.05

Comparing 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 trees

since 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