The Logistic model for incremental data

The logistic growth curve (sometimes called the Verhulst model as it was first proposed as a model of population growth Pierre Verhulst 1845, 1847) is one of the simplest of the S-shaped growth curves. A generalization of the logistic, which is no longer symmetrical about the point of inflection, was developed by Richards (1959) and is termed the Richards curve or generalized logistic. 

There are a number of different ways that this equation can be written (see Logistic curve). When using incremental data the version used is

where t is age 

where k is the growth rate

b a scaling parameter and

L∞, termed 'L infinity', is the asymptotic length at which growth is zero.