A pond 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.
A pond 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.
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