The nonlinear discrete-time dynamical system The model describing the dynamics of the concentration of medication in the

Question:

The nonlinear discrete-time dynamical system

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 each case, use the Slope Criterion for stability to check the stability of the equilibrium.