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?

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

Given

Population of forest trees

Population of tree in neighboring forest

Step-by-step explanation:

we need to find the population of trees after 100 years

In the given equations, 't' represents the number of years

Substitute t=100 in each equation

The population of neighboring forest is greater .

So , neighboring forest have greater number of tress after 100 years

Now we subtract the population of trees to find how much greater

71 trees are more in neighboring forest after 100 years

Answer :

neighboring forest have greater number of tress after 100 years

71 trees are more in neighboring forest after 100 years

Reference : link

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step-by-step explanation: