Answer
a) $15$ pounds per square inch
b) $3$ pounds per square inch
Work Step by Step
Given \begin{equation}
P(v)=\frac{30}{v}.
\end{equation} a) Find $P(v)$ when $v= 2$.
\begin{equation}
\begin{aligned}
P(2)&= \frac{30}{2}\\
&=15.
\end{aligned}
\end{equation} The pressure of the gas in the balloon is $15$ pounds per square inch when the volume of the balloon is $2$ cubic inches.
b) Find $P(v)$ when $v= 10$.
\begin{equation}
\begin{aligned}
P(10)&= \frac{30}{10}\\
&=3.
\end{aligned}
\end{equation} The pressure of the gas in the balloon is $3$ pounds per square inch when the volume of the balloon is $10$ cubic inches.
