I suppose the go to tool for fitting non-linear models in R is nls of the stats package. In this post I will show an alternative approach with Stan/RStan, as illustrated in the example, Dugongs: “nonlinear growth curve”, that is part of Stan’s documentation.
The original example itself is taken from OpenBUGS. The data describes the length and age measurements for 27 captured dugongs (sea cows). Carlin and Gelfand (1991) model the data using a nonlinear growth curve with no inflection point and an asymptote as \(x_i\) tends to infinity: