A student investigates the discharging behavior of a circuit containing a capacitor of unknown capacitance \(C\) and a resistor of known resistance \(R\). The capacitor is fully charged and then allowed to discharge through the resistor while a sensor records the current \(I\) as a function of elapsed time \(t\). The theoretical relationship for the discharging current is given by \(I = I_0 e^{-t/(RC)}\), where \(I_0\) is the initial current. To extract an experimental value for \(C\) from a linear fit of the data, which quantities should be plotted on the vertical and horizontal axes, and how is \(C\) determined from the slope \(m\) of the best-fit line?