College Algebra, Chapter 3, 3.6, Section 3.6, Problem 62

Suppose a spherical balloon.
a.) Fund a function $f$ that models the radius as a function of time.

$
\begin{equation}
\begin{aligned}
r (t) &= (1)t\\
\\
r (t) &= t
\end{aligned}
\end{equation}
$


b.) Find a function $g$ that models the volume as a function of the radius.
$\displaystyle V(r) = \frac{4}{3} \pi r^3$

c.) Find $g \circ f$. What does this function represent?

$
\begin{equation}
\begin{aligned}
g \circ f &= V(r(t))\\
\\
g \circ f &= V(t)\\
\\
g \circ f &= \frac{4}{3} \pi t^3
\end{aligned}
\end{equation}
$


It represent the increasing rate of volume with respect to time.