AP Calculus AB 7.1 Modeling Differential Equations Question Bank

Practise differential-equation modeling questions by translating rates, growth and physical relationships into derivative expressions.

Exam points

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

[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?

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

$\frac{d M}{d t}=k \sqrt{t}$

$\frac{d M}{d t}=k \sqrt{M}$

$\frac{d M}{d t}=\frac{k}{\sqrt{M}}$

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FUN-7.A—Interpret verbal statements of problems as differential equations involving a derivative expression question 1