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Homework Statement
A pond initially contains 1,000,000 gal of water and an unknown amount
of an undesirable chemical. Water containing 0.01 gram of this chemical per
gallon flows into the pond at a rate of 300 gal/hour. 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 dierential equation for the amount of the chemical 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?
Homework Equations
The Attempt at a Solution
t (hours)
y (grams)
y(0) = y0
dy/dt = 3g/hr - (??) -- How do I determine the rate at which it's flowing out if I don't know the initial value?