AP Calculus BC 7.9 Logistic Models Overview

Interpret logistic differential equations through carrying capacity, limiting population and the point of greatest growth.

Exam points

identify the governing calculus relationship in the problem
justify the result with symbolic, graphical or contextual evidence

Covered syllabus points

FUN-7.H—Interpret the meaning of the logistic growth model in context

[Maximum number: 1]

In a community of 6000 people, the number of people informed about an upcoming event after t weeks is modeled by a function P(t) that satisfies a logistic differential equation. When 1000 people are informed of the event, the rate of growth of informed people is 100 people per week. If all people in the community eventually become informed of the event, which of the following differential equations describes the situation?

$\frac{d P}{d t}=0.12 t\left(1-\frac{t}{1000}\right)$

$\frac{d P}{d t}=0.12 t\left(1-\frac{t}{6000}\right)$

$\frac{d P}{d t}=0.12 P\left(1-\frac{P}{5000}\right)$

$\frac{d P}{d t}=0.12 P\left(1-\frac{P}{6000}\right)$

Figure for Question 7.9 Logistic Models with Differential Equations question 1 — AP Calculus BC

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Covered syllabus points

7.9 Logistic Models with Differential Equations question 1