SOLUTION: Solve the problem. The logistic growth function f(t) = 400/1+9.0e-0.22t describes the population of a species of butterflies after they are introduced to a non-threatening hab

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Solve the problem. The logistic growth function f(t) = 400/1+9.0e-0.22t describes the population of a species of butterflies after they are introduced to a non-threatening hab      Log On


   

Question 617971: Solve the problem.
The logistic growth function f(t) = 400/1+9.0e-0.22t describes the population of a species of butterflies after they are introduced to a non-threatening habitat. How many butterflies are expected in the habitat after 12 months?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
based on this equation, the limiting size appears to be 400, assuming the equation is:
f(t) = 400 / (1+9.0*e^(-.22t))
presumably t represents number of months.
i'll assume that.
the following table of values based on the assumed equation is shown below:
x       y = 400 / (1+9*e^(-.22t))
0       40
1       49
2       59
12      244 *****
24      383
36      399
38      400

after 38 months the rounded up number stabilize at 400 and go no higher.
this is the maximum size of the population based on the equation.
a graph of this equation looks like this:
graph%28600%2C600%2C-10%2C50%2C-20%2C500%2C400%2F%281%2B9%2Ae%5E%28-.22x%29%29%29