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AP Calculus AB 7.1 Differential-Equation Models Review

Review AP Calculus AB 7.1 by translating verbal growth, motion, or area relationships into differential equations with correctly named rates.

Syllabus
Effective Fall 2025
Course
AP Calculus AB

Exam points

  • translate a verbal situation into a differential equation involving a derivative
  • identify variables, rates and initial conditions in a model

Covered syllabus points

FUN-7.A—Interpret verbal statements of problems as differential equations involving a derivative expression

7.1 Modeling Situations with Differential Equations question 1

[Maximum number: 1]

As an ice block melts, the rate at which its mass, M, decreases is directly proportional to the square root of the mass. Which equation describes this relationship?

A

M(t)=kt\sqrt{M(t)}=k t

B

dMdt=kt\frac{d M}{d t}=k \sqrt{t}

C

dMdt=kM\frac{d M}{d t}=k \sqrt{M}

D

dMdt=kM\frac{d M}{d t}=\frac{k}{\sqrt{M}}

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