A cylindrical tank is initially filled with water to a depth of 16 feet. A valve in the bottom is opened and the water runs out. The depth, h, of the water in the tank decreases at a rate proportional to the square root of the depth. Write a differential equation that expresses this relationship.

A cylindrical tank is initially filled with water to a depth of 16 feet. A valve in the bottom is opened and the water runs out. The depth, h, of the water in the tank decreases at a rate proportional to the square root of the depth; that is Solve the following differential Equation

where k is a constant. Find the solution of the differential equation in terms of k.

hkdtdh

After the valve is opened, the water falls to a depth of 12.25 feet in 8 hours. Find the value of k with 0< k < 1.

How many hours after the valve was first opened will the tank be completely empty?