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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?

Respuesta :

marcthemathtutor

Answer:

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

[tex]A(t)= 115(1.025)^t[/tex]

Population of tree in neighboring forest

[tex]B(t)=82(1.029)^t[/tex]

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

[tex]A(100)= 115(1.025)^{100}=1358.58\\B(100)=82(1.029)^{100}=1430.050\\[/tex]

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

[tex]1430.0503-1358.58=71.47[/tex]

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 : https://brainly.com/question/13977748

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