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?

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

Step-by-step 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 ". 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:

see attached

step-by-step explanation:

given the function as;

write the equation replacing f(x) with y

form   and fill a table containing values of y with corresponding values of x

you can take a range for   values of x as -3≤x≤3

solving for x=-3

for x=-2

repeat the same procedure to get the values of y for the remaining ,x=-1 to x=3

plot the values of y against values   of x and obtain the following graph

what is the model?

step-by-step explanation: