Question: Suppose that fraction used = 0.5 / 1.0 + 0.4Mt. Write the discrete-time dynamical system, solve for the equilibrium, and compare with M* = 2.0

Suppose that fraction used = 0.5 / 1.0 + 0.4Mt. Write the discrete-time dynamical system, solve for the equilibrium, and compare with M* = 2.0 for the basic model. The model describing the dynamics of the concentration of medication in the bloodstream, Mt+1 = 0.5Mt + 1.0, becomes nonlinear if the fraction of medication used is a function of the concentration. In the basic model, half is used no matter how much there is. More generally, new concentration = old concentration - fraction used × old concentration + supplement Suppose that the fraction used is a decreasing function of the concentration. The above problem looks at two cases. In each, find the equilibrium concentration.

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