We usually charge a capacitor through a resistor:
Given that the voltages across the power supply, capacitor (capacitance $C$) and resistor (resistance $R$) are $V_S$, $V_C$ and $V_R$ respectively, we can write a relationship relating these voltages during capacitor charging: $$ \begin{equation}\begin{aligned} V_C=V_S(1-e^{-\frac{t}{CR}})\\ \end{aligned}\end{equation} $$
This relationship can be graphed as:
Charge stored in the capacitor behaves in a similar way: $$ \begin{equation}\begin{aligned} Q=Q_0(1-e^{-\frac{t}{CR}})\\ \end{aligned}\end{equation} $$
The current approaches zero: $$ \begin{equation}\begin{aligned} I=I_0e^{-\frac{t}{CR}}\\ \end{aligned}\end{equation} $$