Logistic Models

Question

The maximum number of possums that can be supported by the environment of a national park is estimated to be 3000. When first counted, there are found to be 1200 possums, but after 4 months the number has grown to 1300. Find the parameters for the logistic model and use it to predict the number of possums after 1 year

Answer 1

I don't know which letters your book uses, but I've seen the logistic model written down as

 

                c

f(t) = -------------

            1 + a e^-kt

 

in a precalculus book.  c is the limit to growth, so c = 3000.

 

Initial population is 1200, so f(0) = 1200, so c/(1+a) = 1200.

 

If t is the number of months, then f(4) = 1300, so c/(1+ae^-4k) = 1300.

 

This should be enough information to solve for c, a, and k.  Once you have those, you'll get a number for f(12).