A few weeks ago some on this list stated their opinion that the
exponential function and its properties should be taught to all
students, specifically for its application to the prediction of
human population growth. For those of you born before 1945, you
might remember a prediction made in 1968 by Paul Ehrlich in his
book "The Population Bomb." In it he says that population is
doubling every 37 years and: "If growth continued at that rate
for about 900 years, there would be some 60,000,000,000,000,000
people on the face of the earth. Sixty million billion people.
This is about 100 persons for each square yard of the Earth's
surface, land and sea." Of course, we would all die long before
then. But, why use the number then, except that numbers have
prestige. He then called for the creation of a "powerful government
agency" which would impose solutions such as "compulsory birth
regulation" and "the addition of temporary sterilants to water
supplies or staple food." He also recommended that countries like
India, whose population problems were hopeless, should not be given
food. 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.