 Solution

The transformation $t=(x-\overline{x})/s_x$ centers day at zero and measures it in standard-deviation units. It reduces numerical scale differences and makes the intercept-like parameter refer to the middle of the observed time range. In nonlinear regression this can reduce posterior parameter dependence and improve Markov chain Monte Carlo mixing. It also makes priors on the growth coefficient easier to interpret; it does not change the curve family.