A pond initially contains 7800 gallons of water and 200 grams of an undesirable chemical. Water containing 0.34 grams of this chemical per gallon flows into the pond at a rate of 95 gallons per hour. Water flows out of the pond 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, c (in grams), in the pond at time t (in hours). (b)How much of the chemical will be in the pond after a very long time?
I have solved the part (a) which is $\frac{dc}{dt} = 32.3-\frac{95c}{8000}$. And when I doing the second part, I know it is looking for $\lim_{t \to \infty}c(t)$. And my thought is when $\frac{dc}{dt}=0$, I can get the solution. So $c = \frac{0.34*95}{\frac{95}{8000}}=2720$. But the answer for the part (b) is wrong. I don't know how to fix it.
After a long time the concentration is not changing, so the concentration in the pond is the same as the concentration of the inflow. That will let you solve part b even if your solution to part a is not correct.