6.5 Logistic Growth

I. Logistic Growth and Decay Exponential growth assumes unlimited growth, which is realistic for a short period of time. Usually, there will be a decrease in the rate of growth as time passes on due to such limiting factors as disease, food supply, etc. i.e., there exists a carrying capacity or a maximum population M. The relative growth rate is proportional to .

We start with a logistic differential equation We start with a logistic differential equation. Its solution is a logistic growth model.

II. Partial Fraction Review Add the following fractions: What if we want to go backward. i.e., we are given the fraction above and we need to separate it into two Partial Fractions?

Now…Separate the following into two partials:

III. Example Ex. 2 on page 343- National Park, 10 bears present now, maximum population of 100 grizzlies, k=.1. When will there be 50 bears present?

Now to finally solve the problem!!!!!