If a cylindrical water tank holds 5000 gallons, and the water drains from the bottom of the tank in 40 minutes, then Torricelli’s Law gives the volume V of water remaining in the tank after t minutes as

V = 5000(1 – 1/40 t)² 0 ≤ t ≤ 40

Find the rate at which water is draining from the tank after
(a) 5 min,

(b) 10 min,

(c) 20 min, and

(d) 40 min. At what time is the water flowing out the fastest? The slowest? Summarize your findings.