A mixer holds a solution whose concentration is

MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

C(t)=\dfrac{m(t)}{V(t)}

. At a particular moment,

m=500\text{ g}

and

V=250\text{ L}

. The salt is being added at

\dfrac{dm}{dt}=2\text{ g min}^{-1}

while the solution drains at

\dfrac{dV}{dt}=-4\text{ L min}^{-1}

. Determine

\dfrac{dC}{dt}

at that moment (in

\text{g L}^{-1}\text{ min}^{-1}

). (a)

0.032

(b)

0.04

(c)

-0.04

(d)

-0.024