Bacteria Growth Problem

Suppose we have a population of bacteria in a petri dish. We want to model the number of bacteria as a function of time, \(y(t)\). Assume at time 0, \(y_0\) bacteria are in the dish.
Also assume the dish can only hold \(M\) bacteria. See DE example

A full four section paper (be sure it is at least your second draft) is due on Monday.