(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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?

2. Relevant equations

3. The attempt at a solution

t (hours)

y (grams)

y(0) = y_{0}

dy/dt = 3g/hr - (??) -- How do I determine the rate at which it's flowing out if I don't know the initial value?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Differential Equations - Word Problem

**Physics Forums | Science Articles, Homework Help, Discussion**