A salt tank contains 100 liters of pure water at time t= 0, when salty water begins flowing into tank at 2 liters per second. The incoming liquid contains 1/2 kg of salt per liter. The well-stirred liquid flows flows out of the tank at 2 liters per second.
1) Model the situation with a first order DE, and find the amount of salt in the tank at any time.
2) Suppose that the at time t = 20 seconds 5 kg of salt is instantaneously dumped into the tank. Modify the DE from the previous part (hint: a delta function appears on the right side). Solve the resulting DE using laplace transform. Plot the s

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