Science:Math Exam Resources/Courses/MATH102/December 2017/Question 14 (a)/Statement

The males of the magnificent frigatebirds have a bright red throat pouch that gets inflated like a balloon to attract females during mating season. Suppose that the rate of change of the volume during inflation is $$V^{\prime }(t)=\frac{100\pi }{15}(20-t)$$ measured in ${\mathrm{c}\mathrm{m}}^3/\mathrm{m}\mathrm{i}\mathrm{n}$ for $0\le t\le 20$. At $t=0\mathrm{m}\mathrm{i}\mathrm{n}$, the pouch is empty.

(a) Find the function $V(t)$ for the volume at time $t$ during inflation.

(Hint: consider a simple antiderivative.)