6.3 Growth Models

Growth follows many different patterns. Some are linear, but more often they are not. For instance, Moore's Law describes the roughly exponential growth of semiconductor capacity (e.g., integrated circuit components per unit size or memory per dollar), a trend that has persisted for over half a century. Industry has used this trend to “roadmap” the timing of future capabilities (Semiconductor Industries Association 2010). Roadmapping is briefly treated in Chapter 11. More typically, exponential growth patterns do not hold for such extended periods; rather, growth confronts some form of limit (e.g., physical, technological, economic, or social).

More commonly, technological capabilities follow S-shaped growth curves. These are characterized by slow initial growth, followed by a period of rapid (almost exponential) growth, and finally by an asymptotic tapering to a limit. Market penetration curves also often follow similar trajectories, as do many biological system characteristics (e.g., the weight of a corn plant as it grows). There are several important mathematical formulations for these curves.

6.3.1 The Models

While almost any conceivable growth curve might fit a special case, the focus here is on those most often found to describe technological innovation—the S-curves. The popular concept of exponential growth usually is not sustainable, although Moore's Law has hitherto been an important exception.

S-shaped or logistic curves are loosely modeled on biological ...

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