Problem
The volume $V(r)$ (in cubic meters) of a spherical balloon with radius $r$ meters is given by $V(r)=\frac{4}{3} \pi r^{3}$. The radius $W(t)$ (in meters) after $t$ seconds is given by $W(t)=5 t+3$ Write a formula for the volume $M(t)$ (in cubic meters) of the balloon after $t$ seconds. It is not necessary to simplify. \[ M(t)= \]
Solution
Step 1 ：We are given two functions, $V(r)$ and $W(t)$. We are asked to find a formula for the volume $M(t)$ of the balloon after $t$ seconds.
Step 2 ：Since the volume of the balloon is a function of its radius, and the radius is a function of time, we can substitute $W(t)$ into $V(r)$ to get $M(t)$.
Step 3 ：Final Answer: \(\boxed{M(t)=V(W(t))=\frac{4}{3} \pi (5t+3)^{3}}\)
