Question: Consider the discrete-time dynamical system for medication given by M t + 1 = 0.5M t + 1.0 with M 0 = 3. 1. Find

Consider the discrete-time dynamical system for medication given by Mt + 1 = 0.5Mt + 1.0 with M0 = 3.

1. Find the equilibrium.

2. The solution is Mt = 2.0 + 0.5t × 3.0. Find the limit as t → ∞.

3. How long will the solution take to be within 1 % of the equilibrium?

4. What are two ways to show that this equilibrium is stable?

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