A $10$ Superscript negative $9-$F capacitor $(1$ nanofarad$)$ is charged to $100$ V and then disconnected. One can model the charge leakage of the capacitor with a RC circuit with no voltage source and the resistance of the air between the capacitor plates. On a cold dry day, the resistance of the air gap is $5$times$10$ Superscript $13$ Upper Omega; on a humid day, the resistance is $7$times$10$ Superscript $6$ Upper Omega. How long will it take the capacitor voltage to dissipate to half its original value on each day?