Answer
(a) Linear function: $$V(t) = 0.5t + 2$$
(b) It takes 26 seconds to completely fill the baloon.
Work Step by Step
(a) Linear function: $V(t) = at + b$
Since the rate of change of volume is :$0.5 \space ft^3/s$, a = $0.5$
Since the initial volume is $2 \space ft^3$: $b = 2$
Thus:
$$V(t) = 0.5t + 2$$
(b) Solve for $t$, and calculate its value when $V(t) = 15$
$$V(t) - 2 = 0.5t \longrightarrow \frac{V(t) - 2}{0.5} = t$$ $$\frac{15 - 2}{0.5} = t$$ $$t = \frac{13}{0.5} = 26$$