Question

The number of trees in a forest follows the logistic growth function f(t)=32000/1+12.8e^-0.065t where t is the time in years. What is the maximum number of trees in the forest?

Answer 1

Maximum number of trees will be 32000 as time grows to infinity

Explanation:

Recall that the expression for logistic growth includes a quotient of a number (in our case 32000) divided by "1 + a number that approaches zero with time (in our case
`e^(-0.065\,t)`". This is a decaying exponential function, that as "t" grows approaches zero.

Therefore, as the time increases, the denominator becomes closer and closer to 1 (one) due to the exponential factor approaching zero that is added to "1".

Then the maximum will be obtained when the quantity in the denominator becomes as small as possible, and that is as time grows. Reaching then its maximum as time goes to infinity. And that value is going to be approaching:
`(32000)/(1+0) =32000`