Suppose that per capita production decreases linearly from a maximum of (0) = 4 with slope -0.001.

Suppose that per capita production decreases linearly from a maximum of λ(0) = 4 with slope -0.001. Find λ(b) and the differential equation for b. Is b(t) increasing when b = 1000? Is b(t) increasing when b = 5000?
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.