Alright so I have to model some "real life" situations using Diff Eqs and I'm having a lot of trouble setting up the problem(s). More trouble than I should be having, I think.
The question gives that a tank contains 200L of a dye solution with a concentration of 1 g/L. It's being rinsed with fresh water flowing in at a rate of 2L/min and the dye solution flowing out at 2L/min as well.
I need to find the time elapsed until the concentration of dye in the tank reaches 1% of its original, so 2g/L.
I have Q as the amount of dye in the tank. I have the flow rate of the dye out of the tank, dQ/dt = -2L/min * Q/200L = -Q/100 g/min.
Also I have Q0 = 200 g/L.
I know I'm missing something because my diff eq should be of the form y' + y = g, and I have dQ/dt + Q/100 = 0, which doesn't give me much if I solve it, since the function g(t) = 0. I'm not even sure that I'm setting it up correctly because I'm supposed to be solving for t when the concentration is at a certain point, and my equation mostly regards the rates of flow. Can anyone help me clear this stuff up? Thanks :)
Edit: Solved. Don't think I can delete threads.