At a water tank is being filled by water being pumped into the tank at a volume given by the formula, P(t) = 112t +2000 gallons per minute, where t is in minutes. At the same time the water tank has a leak and the volume of water draining out of the tank is given by the formula L(t) = 15t 2 gallons per minute, where t is in minutes.

a. The volume, V, of water in the tank at any minute, t, is the difference of the volume of the water being pumped into the tank and the volume of water leaking out of the tank. Find the volume function, V(t).

b. The volume function is a quadratic function and so its graph is a parabola. Find the vertex of the volume function V(t). (Round answer to 1 decimal place) Show work.

c. Interpret the vertex in the context of the problem.

d. At what time (t > 0) will the tank be empty? Show work. (Round answer to 1 decimal place)