1. 6.5 Logistic Growth

2. 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

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

4. 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?

6. Now…Separate the following into two partials:

8. 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?

14. Now to finally solve the problem!!!!!