Question 1137502: 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 by jim_thompson5910(35256)   (Show Source):
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Plug t = 100 into A(t)
A(t) = 115*(1.025)^t
A(100) = 115*(1.025)^100
A(100) = 1358.57738
A(100) = 1359
There are roughly 1359 trees in forest A after one hundred years.
Repeat for B(t) as well
B(t) = 82(1.029)^t
B(100) = 82(1.029)^100
B(100) = 1430.05035
B(100) = 1430
There are roughly 1430 trees in forest B after one hundred years.
We see that forest B has more trees after one hundred years.
The difference is 1430 - 1359 = 71 trees, meaning that forest B has 71 more trees compared to forest A after one hundred years.
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