An example of the application of the logistic S-curve can be found in the article: "Applying SegRegA to the annual average temperature trend from 1900 to 2020 in the Netherlands resulting from global warming; analysis by segmented linear regression types and curved functions such as the S-curve, Power curve, generalized quadratic and cubic regressions". Download from: average temperature.pdf

The cubic functions are determined by matrices, determinants and matrix inversion. The third degree polygon can be used as a method to calculate and determine the salt tolerance of crops, see this article published in the International Journal of Agricultural Science and entitled "Crop tolerance to soil salinity, statistical analysis of data measured in farm lands".

An overview of the use of S-curves is given in this text file

A critical review of the use of S-curves for the determination of a salt tolerance index for crops is to be found in this report
          Another critical review of the use of S-curves with the same purpose in various published papers can be seen in this commentary