One widely used nonlinear model of competition is the "logistic" model, where per capita production is a linearly decreasing function of population size. Suppose that the per capita production is

Our models of bacterial population growth neglect the fact that bacteria produce fewer offspring in large populations. The above problem introduce two important models of this process, having the form bt+1 = r(bt)bt
Where the per capita production r is a function of the population size bt. In each case,
a. Graph the per capita production as a function of population size.
b. Write the discrete-time dynamical system and graph the updating function.
c. Find the equilibria.

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r(b)=2 (1- 1.0s lof) × 106