# Chapter 5, Exploration 28

The exploration here shows the the logistic family of functions for values of $$a \in [2.5, 3.3]$$. Use the tool to describe what happens to the dynamics as $$a$$ increases from $$a = 2.5$$ to $$a = 3.3.$$ In particular, what happens to the stability of the fixed point and why? Describe the dynamics near the fixed point for values of $$a$$ less than 3 and for values of $$a$$ greater than 3. The initial condition for this exploration is set to $$x_0 = \frac{1}{2}$$.

a: