If a cylindrical tank holds 100,000 gallons of water, which can be drained from the bottom of the tank in an hour, then Torricelli's Law gives the volume of water remaining in the tank after t minutes as

Question

V(t)=100,000(1-(t/50))^2, 0<=t<=60. Find the rate at which the water is flowing out of the tank (the instantaneous rate of change of V with respect to t) as a function of t.
a)y=(-100000/50)+(100000t/1)
b) y=(-4000/1)+(160t/1)
c)y=(-100000/50)+(80t/1)
d)y= (200000/50)-(200000t/2500)
e)(-4000/1)+(80t/1)

Answer 1

y = dV/dt
= 100,000 * 2(1 - t/50)(-1/50)
= -4000 (1 - t/50)
= -4000 + 80t

This is (e) with all the noise removed