Past exam of the physics A course of the University of Cambridge / 2021 / Paper 1 / Section C / C8 / a / Solution

Take the natural logarithm of the exponential decay model. To keep the logarithm dimensionless, choose the reference rate $R_{\ast }=1\mathrm{count}\mathrm{da}{\mathrm{y}}^{-1}$ and defineThen $y=mx+c$. With time measured in picoseconds, the slope has units ${\mathrm{ps}}^{-1}$ and the intercept is dimensionless. A straight-line linear regression in these variables therefore estimates the inverse mean lifetime and logarithmic normalization.