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

Use $x=t$ in picoseconds and $y=\ln (R/R_{\ast })$. Since the time uncertainty is negligible, only the vertical errors enter. First-order propagation of uncertainty givesThe transformed measurements areThus the logarithmic transformation converts constant fractional rate uncertainties into approximately equal absolute log-rate uncertainties. The equality is the linear error approximation; finite error bars would become slightly asymmetric under an exact logarithm.