Continuing my previous question from today - I should code a program that finds approximate value of the aforementioned differential equation. The full text of the assignment is:
Water purifier with volume $V = 10000 m^3$ has been contaminated by lead, which is disolved in it with volume of $10 g/m^3$. Fresh water is coming to the purifier at the rate of $2 m^3/s$ and it flows out at the same rate. How long will it take for the volume of lead in the water to drop below $10 \mu g/m^3$?
It can be equated as this differential equation: m' = -\frac{m}{V}v
Where $V = 10000 m^3$ - the Volume of the purifier, $v = 2 m^3/s$ - rate of water inflow/outflow and $m$ is the amount of lead present at the given time. I have no problem solving it explicitly.
After separating the variables I get:
$m(t) = Ke^{\frac{-1}{500}t}$
Where $K = 10000$
My problem is that I don't know what to use for the Euler's approximation. The equation stated here does not contain $t$ for the time elapsed - that's something that shows up only after integrating it and separating the variables and since $t$ is what I'm looking for I'm kinda stuck. Any help would be greatly appreciated.