In the RC circuit below the switch is connected to A for a long time such that the capacitor becomes fully charged. The switch is thrown to position B and the voltage across the capacitor recorded as a function of time. The voltage across the capacitor drops from its initial value of $V_C = 15 \:\text V$ down to $7.5 \:\text V$ in a time of $0.22 s$. The value of $R_1 = 50 \:\text k \Omega$ and $R_2 = 75 \:\text k \Omega$.

Given the above information, what is the value of the capacitor?