Suppose a tank is filled initially (at time t = 0) with 100 gallons of fresh clean water. Water containing 10 grams/gallon of chemical pollutants enters the tank at a rate of 2 gallons/day, and the mixture in the well-stirred tank leaves the tank at the rate of 1 gallon/day. (a) Find the amount of water W(t) as a function of time and determine the time when that amount reaches 200 gallons. In order to do this, either set up a very easy ODE for W(t) or use your intuition about the problem. (b) Write down the differential equation that describes the total amount of pollutants P(t) in the tank and find the initial condition P(0) of this quantity at time t = 0. Again, think in terms of rate in minus rate out. (TURN PAGE)