linguistic:voice_change, quality:correction, structural:expansion, structural:reformatting
Reformulation as log-linear growth

If a variable x exhibits exponential growth according to x (t) = x 0 (1 + r) t {\displaystyle x(t)=x_{0}(1+r)^{t}}, then the log (to any base) of x grows linearly over time, as can be seen by taking logarithms of both sides of the exponential growth equation: log x (t) = log x 0 + t ⋅ log (1 + r). {\displaystyle \log x(t)=\log x_{0}+t\cdot \log(1+r).}

This allows an exponentially growing variable to be modeled with a log-linear model. For example, if one wishes to empirically estimate the growth rate from intertemporal data on x, one can linearly regress log x on t.