Linear Differential Equations Tank Problem

Question

So I'm doing the same exact problem as this one:

Now I understood how to set up the problem, I did the integration correctly. My problem is I don't know how to solve for C. I don't know what to plug-in.

So I know x(t) is the amount of toxic substance in the tank right? IN this case why do they use the initial condition x(0) = 0? Is that valid? It seems like they just made it up. Could anyone explain why they did this?

The rest should be explainable.

Thanks

Answer 1

In the first line, they tell you that you start with 10 liters of clean water. That means that the toxic substance in the tank at t=0 is 0 grams.