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Growth Functions

  • Arthur L. Loeb
Part of the Design Science Collection book series (DSC)

Abstract

If you drop a ball from a given height, its velocity will increase at a constant rate called the acceleration of gravity:
$$\frac{{dv}}{{dt}} = g.$$
(17-1)
Integrating, we find that v = gt, assuming that at time t = 0, the moment at which the ball was dropped, the ball had zero velocity. Actually the velocity is itself the rate at which the altitude of the ball decreases:
$$v = - \frac{{dh}}{{dt}}$$
Since \(v = gt,\tfrac{{dh}}{{dt}} = - gt\), and \(h = {{h}_{0}} - \tfrac{1}{2}g{{t}^{2}}\) where h 0 is the initial height from which the ball was dropped at time t = 0.

Keywords

Interest Rate Exponential Function Frictional Force Growth Function Autocatalytical Reaction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

  1. 2.
    Loeb, A. L.: Synergy, Sigmoids and the Seventh-Year Trifurcation, The Environmentalist, 3, 181–186 (1983)Google Scholar
  2. 2a.
    Loeb, A. L.: Synergy, Sigmoids and the Seventh-Year Trifurcation, reprinted Chrestologia, XIV, #2, 4–8 (1989).MathSciNetGoogle Scholar
  3. 4.
    de Sola Price, D. J.: Measuring the Size of Science, Proc. Israel Acad. Science and Humanities, 4, 6 (1969).Google Scholar

Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Arthur L. Loeb
    • 1
  1. 1.Department of Visual and Environmental Studies, Carpenter Center for the Visual ArtsHarvard UniversityCambridgeUSA

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