Answer
(a) $-38.8$ gal/min
$-27.8$ gal/min
(b) $-33.3$ gal/min.
Work Step by Step
(a) Based on the table given by the Exercise, the average rates at which water flows from the tank
(slopes of secant lines) for the time intervals $[10, 15]$ is given by $R_1=\frac{250-444}{15-10}=-38.8$ gal/min
Similarly, the average rates at which water flows from the tank
(slopes of secant lines) for the time intervals $[15, 20]$ is given by $R_1=\frac{111-250}{20-15}=-27.8$ gal/min
(b) The average for the slopes of the secant lines in part (a) is given by $R_a=\frac{-38.8-27.8}{2}=-33.3$ gal/min, which gives an estimate of the rate at which water is flowing from the tank after 15 min.
