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Well, if the exponential function can be used to predict
900 years into the future, it should be possible to retrodict into
the past. If the population now is about 5.4 billion and it is
doubling about every 40 years or so then 600 years ago, in the
fourteenth century the population should have been less than
200,000. But I have read that in the fourteenth century the great
epidemic of black plague killed in Europe alone about 25,000,000
people, making for a world population of 200,000 a truly dismal
retrodiction from the exponetial function. So, I would say that
the exponetial function is quite limited in its applicability to
human population growth, except as a scare tactic via the prestige
of mathematical statements.
James M. Espinosa