Substitution analysis is a well accepted method of technological forecasting in use for 36 years. In these analyses, the Fisher-Pry model was used. The Fisher-Pry model predicts characteristics loosely analogous to those of biological system growth. It results in an S-curve (more formally, sigmoidal curve) familiar to many because the curve is in the shape of an S. These natural growth processes share the properties of relatively slow early change, followed by steep growth, then a turnover as size asymptotically approaches a limit. The relationship between the fraction of total market taken by the new technology, f, is often given as:
f = 1 /(1 + c exp(-bt))
where t is time, and c and b are empirically determined coefficients.