Suppose that fraction used = / 1.0 + 0.1Mt. for some parameter 1. Write the discrete-time dynamical system and solve for the

Suppose that fraction used = β / 1.0 + 0.1Mt. for some parameter β ≤ 1. Write the discrete-time dynamical system and solve for the equilibrium. Sketch a graph of the equilibrium as a function of β. Cobweb starting from M0 = 1.0 in the cases β = 0.05 and β = 0.5.

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.