Charging the Membrane
when time is equal to the time constant, we get the definition for charging the membrane
Charging the Membrane
$$ V_m\left(t=\tau \right) = V_{\infty} * \left(1 - e^{-1}\right) $$
Discharging the Membrane
$$ V_m\left(t=\tau \right) = V_{\infty} * e^{-1} $$