Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life, in Organisms, Cities, Economies, and Companies

by Geoffrey West

population that is growing exponentially is defined mathematically as one in which the rate of increase in its size (per minute, per day, or per year, for instance) is directly proportional to the size of the population that’s already there. Thus the growth rate itself grows even faster the bigger the population. So, for example, when the size of a population undergoing exponential growth doubles, the rate at which it is increasing also doubles, which means that it grows faster and faster the bigger it gets, effectively feeding back and running away with itself. Left unchecked, both the population and its growth rate would eventually become infinitely large.