Answer
$(a) V(t) = 10t + 300$
$(b)$ It takes 100 minutes to completely fill the pond.
Work Step by Step
(a) Linear function: $V(t) = at + b$
Since the rate of change of volume is :$10 \space gal/min$, a = $10$
Since the initial volume is $300 \space gal$: $b = 300$
Thus:
$$V(t) = 10t + 300$$
(b) Solve for $t$, and calculate its value when $V(t) = 1300$
$$V(t) - 300 = 10t \longrightarrow \frac{V(t) - 300}{10} = t$$ $$\frac{1300 - 300}{10} = t$$ $$t = \frac{1000}{10} = 100$$