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AP Calculus AB 7.8 Differential Equation Context

Interpret variables and rates in contextual differential equations, including models where change is proportional to the current quantity.

Syllabus
Effective Fall 2025
Course
AP Calculus AB

Exam points

  • separate variables and integrate both sides of a differential equation
  • apply an initial or particular condition to determine the constant

FUN-7.F—Interpret the meaning of a differential equation and its variables in context question 1

[Maximum number: 1]

A population described by a function P at time t decreases at a rate proportional to P. Which of the following differential equations could describe the rate of change of the population?

A

dPdt=−0.015P\frac{d P}{d t}=-0.015 P

B

dPdt=−0.015P\frac{d P}{d t}=-\frac{0.015}{P}

C

dPdt=−0.02t\frac{d P}{d t}=-0.02 t

D

dPdt=6e−0.02t\frac{d P}{d t}=6 e^{-0.02 t}

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