A pond initially contains 6,000,000 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 200 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?
q= grams
The limiting amount (Does, Does
not) depend on the amount that was present initially.