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AP Calculus BC 7.1 Differential Equation Modeling

Translate statements about changing quantities, proportional rates and contextual relationships into differential equations.

Syllabus
Effective Fall 2025
Course
AP Calculus BC

Exam points

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

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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