Differential Equations and Mathematical Modeling

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AP CALCULUS AB

• Chapter 6
• Differential Equations and Mathematical Modeling
• Section 6.5
• Logistic Growth

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What youll 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.

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Section 6.5 Logistic Growth

• Partial Fraction Decomposition
• If is an improper fraction
• (degree of N(x) gt degree of D(x), divide the
  denominator into the numerator to obtain

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Section 6.5 Logistic Growth

• Example

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Section 6.5 Logistic Growth

• Partial Fraction Decomposition (cont)
• If the degree of the numerator is smaller than
  the degree of the denominator, factor the
  denominator into factors of the form
• For each linear factor the partial fraction
  decomposition would be

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Section 6.5 Logistic Growth

• Example

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Section 6.5 Logistic Growth

• Partial Fraction Decomposition (cont)
• For each quadratic factor of the form where
  
• is non-reducible, the partial fraction
  decomposition must include

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Partial Fraction Decomposition with Distinct
Linear Denominators

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Example Finding a Partial Fraction Decomposition

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Example Antidifferentiating with Partial Fractions

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• Link to Purple Math Partial Fractions

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• Stop and do partial fraction drill sheet

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Logistic Differential Equation

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Example Logistic Differential Equation

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The General Logistic Formula