A student measures the number of undecayed radioactive nuclei \(N\) in a sample as a function of elapsed time \(t\). The decay of the isotope follows the relationship \(N(t) = N_0 e^{-\lambda t}\), where \(N_0\) is the initial number of undecayed nuclei at \(t = 0\) and \(\lambda\) is the decay constant. To determine the half-life \(T_{1/2}\) of the isotope from the experimental data, the student intends to create a linear graph. Which of the following indicates the quantities that should be plotted on the vertical and horizontal axes to yield a straight line, along with the correct expression for \(T_{1/2}\) in terms of the slope \(m\) of the resulting line of best fit?