Per capita production is 2.0 / 1 + bt/1000. Sketch f(bt) for 0 ≤ bt ≤ 2000.
In a discrete-time dynamical system describing the growth of a population in the absence of immigration and emigration, the final population is the product of the initial population and the per capita production. Represent the initial population by bt. In each case, find the final population as a function f(bt) of the initial population, find the derivative, and sketch the function.