If a cylindrical tank holds 140000 gallons of water, which can be drained from the bottom
of the tank in an hour, then Torricelli's Law gives the volume V of water
remaining in the tank after t minutes as
V(t) = 140000\left(1 - \frac{t}{60}\right)^2, \qquad 0 \leq t \leq 60

(a) Find the rate at which the water is flowing out of the tank (the instantaneous rate of change ofV with respect to t ) as a function of t .

(a) Find the rate at which the water is flowing out of the tank (the instantaneous rate of change of

Rate of Flow =

(b) Find both the flow rate and the amount of water remaining in the tank for the times given below.

(i)

Flow rate =

(ii)

Flow rate =

(iii)

Flow rate =

(iv)

Flow rate =

(v)

Flow rate =

(c) At what time is the flow rate the greatest?

At what time is the flow rate the least?

You can earn partial credit on this problem.