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**free_to_fly** a) At a time t=0 a tank contains one unit of water. Water flows out of the tank at a rate proportional to the amount of water in the tank. The amount of water in the tank at time t is y. Show that there's a constant b<1 such that y=b^t.

b) Suppose instead that the tank contains one unit of water at time t=0, but in that addition to the water flowing out as described, water is added at a steady rate a>0. Show that

dy/dx-ylnb=a and hence find y in terms of a, b, and t.