AP Calculus BC 7.9: Logistic Growth Models

Practise AP Calculus BC 7.9 by building logistic differential equations from context and interpreting carrying capacity, limiting values, graphs, and maximum growth rates.

Exam points

Build a logistic differential equation from population size, carrying capacity, and a given rate.
Interpret logistic curves to identify carrying capacity, long-run limits, and the maximum growth rate.

[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 FUN-7.H—Interpret the meaning of the logistic growth model in context question 1 — AP Calculus BC

All question bank results loaded

FUN-7.H—Interpret the meaning of the logistic growth model in context question 1