A cup of tea is 60 degrees hotter than the room at time 0.

A cup of tea is $60$ degrees hotter than the room at time 0. The excess temperature (above the room) at 0, 5, 10, ..., 30 minutes is $60 e^{-t/12}$ degrees. Draw the excess temperature against time in two panels: one with a linear scale and one with a log scale. On the log panel, the points should lie on a straight line. Use np.polyfit(t, np.log(excess), 1), which gives the slope and the intercept of the best straight line through the points of $\ln(\text{excess})$, to find the time constant, which is $-1 / \text{slope}$.