Originally Posted by braddy
Looks OK to me, that is exactly what the problem says, and is one of
the common models for this sort of problem.
It essentially means some thing like:
Everyone not aware of the product has an equal chance of becoming aware
of it in unit time, so the infection rate is proportional to the number not
infected. Then we treat the population as though its a continuous variable
rather than discrete, which give us your ODE:
with initial condition .