Suppose that fraction used = 0.5 / 1.0 + Mt for some parameter . Write the discrete-time dynamical system and solve for the equilibrium. Sketch

Suppose that fraction used = 0.5 / 1.0 + αMt for some parameter α. Write the discrete-time dynamical system and solve for the equilibrium. Sketch a graph of the equilibrium as a function of α. What happens when α > 0.5? Can you explain this in biological terms? Cobweb starting from M0 = 1.0 in the cases α = 0.1 and α = 1.0.
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.