A pond initially contains 8,000,000 gal of water and an unknown amount of an undesirable chemical. Water containing 0.04 grams of this chemical per gallon flows into the pond at a rate of 100 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.
Let q(t) denote the amount of chemical in the pond at time t. Use q as q(t). Do not use thousands separator in the answer field.
dq/dt = 80000 grams/hour
(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?
q = 40,000 grams