Answer
(a) $50,000\ gal$ and $30,000k\ gal$.
(b) during the 1st and 4th days.
(c) $45,000\ gal$, $40,000\ gal$.
(d) $5000\ gal/day$
Work Step by Step
(a) Based on the given graph, the initial and final amounts of water contained in the pool can be estimated to be $50,000\ gal$ and $30,000k\ gal$.
(b) Based on the given graph, the amount of water in the pool remain constant during the 1st and 4th days.
(c) For $f(2)$, locate $x=2$ and read the y-coordinate to get $f(2)\approx45,000\ gal$. For $f(4)$, locate $x=4$ and read the y-coordinate to get $f(4)=40,000\ gal$.
(d) During $[1,3]$, identify the two endpoints as $(1,50000)$ and $(3,40,000)$, we can find the slope as $m=\frac{40000-50000}{3-1}=-5000$ which gives the rate of draining as $5000\ gal/day$