A two-way pump attached to a reservoir pumps water into and then out of the reservoir at a rate of 2000 sin(t) liters per hour, where ț is measured in hours. At time t = 0 a valve at the bottom of the reservoir is opened and it begins to drain at a rate proportional to the amount of water in the reservoir. The reservoir initially contains 10000o liters of water, and the initial outflow rate is measured to be 1000 liters per hour. A. Establish an initial value problem that models the volume of water in the reservoir at time t. B. Solve initial value problem to find the number of liters of water in the reservoir at time t. C. Estimate the point in time when the reservoir first run dry.

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