Apond initially contains 1,000,000 gal of water and an unknown amount of an undesirable chemical. water containing 0.01 grams of this chemical per gallon flows into the pond at a rate of 300 gal/h. the mixture flows out at the same rate, so the amount of water in the pond remains constant. assume that the chemical is uniformly distributed throughout the pond a. write a differential equation for the amount of chemical in the pond at any time. b. how much of the chemical will be in the pond after a very long time? does this limiting amount depend on the amount that was present initially? c. write a differential equation for the concentration of the chemical in the pond at time t. hint: the concentration is c- a/v -a(t)/106