Consider the dynamical system \begin{align*} w_{ n+1} - w_n &= 1.7 w_n\left(1-\frac{ w_n }{ K }\right) \quad \text{for $n=0,1,2,3, \ldots$} \end{align*} where $K$ is a positive parameter.

Find all equilibria and determine their stability.

Does the stability of any of the equilibria depend on the value of $K$?

Consider the dynamical system \begin{align*} x_{ t+1} - x_t &= r x_t\left(1-\frac{ x_t }{ 8000 }\right) \quad \text{for $t=0,1,2,3, \ldots$} \end{align*} where $r$ is a nonzero parameter.

The system has two equilibria. What are they?

For each equilibrium, determine the range of $r$ for which the equilibrium is stable.