= Solution
Take the <natural logarithm> of the <exponential decay> model. To keep the logarithm dimensionless, choose the reference rate $R_*=1\,\mathrm{count\,day^{-1}}$ and define
$$
\boxed{x=t,\qquad y=\ln(R/R_*),\qquad
m=-\frac1\tau,\qquad c=\ln(R_0/R_*).}
$$
Then $y=mx+c$. 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.
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