(This question is not specific to biology, but I was just wondering about a common way that people view differential equations in biology.)
Some simple biological differential equations take the form $ \frac{dx}{dt}=-cx$, where the solution is $ x=x_0e^{-ct}$, $x_0$ being an initial concentration of particles.
I usually see problems treat $x$ as a concentration of particles, but is there any particular reason why we can't treat $x$ as a number of particles? Some of my friends said there may be a problem if we treat $x$ as a number of particles, but I couldn't understand their explanation.