To understand anything about RC filters we should begin from the RC oscillator. This neat peace of circuit has some interesting propreties, all simple to derive. Let's start from the resistance and capacitor formulas:

$$-\mathrm{C}\frac{\mathrm{dV}}{\mathrm{dt}}=\mathrm{I}$$ $$\mathrm{V}=\mathrm{RI}$$

    +----------+
    |          |
    |         +-+ 
   ---        | |
 C            | | R
   ---        | | 
    |         +-+
    |          |
    +----------+
			

From these simple formulas we can derive that, if an initial voltage on the capacitor is present, the circuit will have a time evolution of:

$$\frac{\mathrm{V}}{\mathrm{R}}=\mathrm{-C}\frac{\mathrm{dV}}{\mathrm{dt}}$$
$$-\frac{1}{\mathrm{RC}}\mathrm{dt}=\frac{\mathrm{dV}}{\mathrm{V}}$$
$$-\frac{\mathrm{t}}{\mathrm{RC}}=\mathrm{Log(V\; -\; V0)}$$
$${\mathrm{V0\; e}}^{\frac{\mathrm{-t}}{\mathrm{RC}}}=\mathrm{V}$$