4. A water tank with cross section A is filled with water to height H. The water is discharged through an opening of cross section B at the base of the container. Torricelli's Law states that the height h(t) of the water at time t satisfies the differential equation dh B dt A V2gh, where g > 0 is a constant (a) Based on the differential equation, is h increasing or decreasing, and why? Does this agree with your intuition about whether the height h(t) should be increasing or decreasing? (b) Find an expression for h(t) in terms of t, A, B, g, and H (you should have no constant of integration in your final answer). (c) Find the time T it takes for the tank to empty