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 [math] of water remaining in the tank after [math] minutes as [math]

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

Rate of Flow =

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

(i) [math]:

Flow rate = Amount of water remaining =

(ii) [math]:

Flow rate = Amount of water remaining =

(iii) [math]:

Flow rate = Amount of water remaining =

(iv) [math]:

Flow rate = Amount of water remaining =

(v) [math]:

Flow rate = Amount of water remaining =

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

[math] =

At what time is the flow rate the least?

[math] =