Suppose that per capita production increases linearly with (0) = -5 and a slope of 0.001. Find

Suppose that per capita production increases linearly with λ(0) = -5 and a slope of 0.001. Find λ(b) and the differential equation for b. Is b(t) increasing when b = 1000? Is b(t) increasing when b = 3000?
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.