Problem $5$:

For the following circuit find:

$C=1\mathrm{.}0F$

$R=100k$

a$)$ The time constant of the circuit.

b$)$ The time $t$ that it takes for the current through the resistor to drop to $10\%$ of its value when the switch is Opened

c$)$ At time $t$ from part $b$ above how much charge remains on the capacitor?

Please show and explain all work, thank you!