A pond initially contains 5,000,000 gal of water and an unknown amount of an undesirable chemical. Water containing 0.02 grams of this chemical per gallon flows into the pond at a rate of 100 galh. 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.
(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?
The limiting amount (Click for List)does or does not depend on the amount that was present initially?