## 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

Explain why the differential equation, \(\displaystyle \frac{dy}{dt}=ky\Big(1-\frac{y}{M}\Big)\), makes sense for this situation.

Find an equation for \(y(t)\) in terms of \(k, M, y_0\), and \(t\). Be sure your work is easy to follow.

Test your work by graphing (e.g with Desmos) your solution where \(y_0=.25\), \(M=1\), and \(k=4\). See DE example for a complete graph.

A full four section paper (be sure it is at least your second draft) is due on Wednesday. You may hand-write the solution section. Be sure to include a picture of your Desmos graph.

*Title*
*Problem*
*Approach*
*Solution*
*Final Thoughts*