Chapter 2
Models of Growth: Rates of Change
Writing in 1798, the British economist Thomas Malthus made some dire predictions about the human population of the Earth. His concept of the problem is shown in Figure 1.
Figure 1 Food supply and
population as functions of time.
Which graph do you think is
the food supply? Why?
Malthus observed that the food supply was growing only linearly as a function of time and the population at a much faster rate. Thus, even if the food supply were more than adequate at the moment, population growth would soon outstrip the ability of people to feed themselves. Unless some man-made or natural disaster wiped out large portions of the population first, widespread famine would be the inevitable result.
Malthus may well have been wrong about both the food supply and the population. Nevertheless, we have been hearing, at least since the 1960's, even more dire predictions about overpopulation early in the 21st century, so it is clearly important to know what growth rates tell us about population size and overuse of essential resources.
To analyze the population problem as Malthus saw it, we must understand and compare the growth rate of the world's human population and the growth rate of the food supply. Growth rates are examples of rates of change of functions, and the study of rates of change of functions is the subject of the first course in calculus.
