The Law of Exponential Growth: Evidence, Implications and Forecasts.

Abstract

THE NOTION THAT KNOWLEDGE grows exponentially seems to have first appeared in a short story by Sir Arthur Conan Doyle, "The Great Keinplatz Experiment," which contains the statement, "Knowledge begets knowledge as money bears interest."'Thus, knowledge growth is likened to compound interest-the increase at any time is a fixed percentage of the current amount.This type of growth is described mathematically by an exponential function.If F(t) represents the size at time t , the exponential function, or law, may be expressed aswhere a is the initial size-i.e., at time t =O-and b, the continuous growth rate, is related to the percentage by which the size increases each year (or other appropriate time unit).Specifically, this percentage is given by r=lOO(eb-l), or, approximately, r=100b.For example, if the amount of knowledge at some initial time is a=10,000 and the growth rate is approximately r =10 percent, then after 10years the amount of knowlege will be F(I0) = 10,OOOe""'O'= 27,183.After 100 years the amount will be F(100)= 10,OOOeo~"'oo' = 220,264,660.