The concentration of a gas in a spherical balloon is parts per million

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

The concentration of a gas in a spherical balloon is

C(V)=\dfrac{100}{V}

parts per million, where

V

is the volume in cubic centimeters. Volume depends on the radius

r

V=\dfrac{4}{3}\pi r^{3}

, and the radius varies with time as

r(t)=t+1

cm for

t

in seconds. Find

\dfrac{dC}{dt}

t=2\text{ s}