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 Monday.

• Title
• Problem
• Approach
• Solution
• Final Thoughts