1. CHAPTER 6: DIFFERENTIAL EQUATIONS AND MATHEMATICAL MODELING SECTION 6.5: LOGISTIC GROWTH AP CALCULUS AB

2. What you’ll learn about How Populations Grow Partial Fractions The Logistic Differential Equation Logistic Growth Models … and why Populations in the real world tend to grow logistically over extended periods of time.

3. Section 6.5 – Logistic Growth Partial Fraction Decomposition 1. If is an improper fraction (degree of N(x) > degree of D(x), divide the denominator into the numerator to obtain

4. Section 6.5 – Logistic Growth Example

5. Section 6.5 – Logistic Growth Partial Fraction Decomposition (cont) 2. If the degree of the numerator is smaller than the degree of the denominator, factor the denominator into factors of the form a) For each linear factor the partial fraction decomposition would be

6. Section 6.5 – Logistic Growth Example:

7. Section 6.5 – Logistic Growth Partial Fraction Decomposition (cont) b) For each quadratic factor of the form where is non-reducible, the partial fraction decomposition must include

8. Partial Fraction Decomposition with Distinct Linear Denominators

9. Example Finding a Partial Fraction Decomposition

10. Example Antidifferentiating with Partial Fractions

11. Link to Purple Math Partial Fractions

12. Stop and do partial fraction drill sheet

13. Logistic Differential Equation

14. Example Logistic Differential Equation

15. The General Logistic Formula