Exercises 55 60 introduce a model for population growth

Chapter 5, Problem 55

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Exercises 55 60 introduce a model for population growth that takes into account limitations on food and the environment. This is the logistic growth model, named and studied by the nineteenth century Belgian mathematician and sociologist Pierre Verhulst. (The word logistic has Latin and Greek origins meaning calculation and skilled in calculation, respectively. However, that is not why Verhulst named the curve as he did. See Exercise 56 for more about this.) In the logistic model that well study, the initial population growth resembles exponential growth. But then, at some point, owing perhaps to food or space limitations, the growth slows down and eventually levels off, and the population approaches an equilibrium level. The basic equation that well use for logistic growth is N P 1 aebt 5730 ln 1N/9202 ln 11/22 where N is the population at time t, P is the equilibrium population (or the upper limit for population), and a and b are positive constants. 55