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

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.

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

Section 6.5 – Logistic Growth Example

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

Section 6.5 – Logistic Growth Example:

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

Partial Fraction Decomposition with Distinct Linear Denominators

Example Finding a Partial Fraction Decomposition

Example Antidifferentiating with Partial Fractions

Link to Purple Math Partial Fractions

Stop and do partial fraction drill sheet

Logistic Differential Equation

Example Logistic Differential Equation

The General Logistic Formula