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 per capita production has a maximum at λ(0) = 1 and that it decreases with a slope of -0.002. Find λ(b) and the differential equation for b. Is b(t) increasing when b = 10? Is b(t) increasing when b= 1000?
The simple model of bacterial growth assumes that per capita production does not depend on population size.
The above problems help you derive models of the form
db/dt = λ(b)b
where the per capita production λ. is a function of the population size b.