AP Calculus BC 7.1: Modeling Situations with Differential Equations

Practise AP Calculus BC 7.1 questions by translating verbal rates of change into differential equations that connect a quantity with its derivative.

Exam points

Translate direct proportionality between a rate and √M into an equation such as dM/dt = k√M

[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