Question

For each year , the population of a forest of trees is represented by 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 1

Answer:  Forest B has 71 more trees than forest A after 100 years.

Step-by-step explanation:

I'm assuming that both functions should read as follows:  (the time, t, is shown as a power, instead as a multiplication).

A(t)=115(1.025)^t

B(t)=82(1.029)^t

Although A starts out with more trees (115), B is growing at 2.9% per year [1.029], versus 2.5% [1.025]for A.

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

A(100) = 1359

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

B(100) = 1430

Forest B has 71 more trees than forest A after 100 years.