ABSTRACT

This paper extends the discrete-time logistic model, which allows backwarding in time, to another model in the continuous-time domain. The extension uses the latest features of the successive product operations, that make possible to extend the domain of an already known successive product with integer arguments to another one, whose arguments can be any real value, uniquely and consistently with functions already known by other domain extension techniques. This approach not only uses a closed expression capable of backwarding to generations before the first observed one but also allows to quantify the population at any intermediate moment between any two generations. To illustrate the advantages of this extension methodology, a typical case of logistic growth of the literature is revisited, extending its time domain from integer to real values. In addition to other benefits resulting from the successive product extension methodology, an increase in accuracy is confirmed by comparison with an usual interpolation method.