Suppose that fraction used = / 1.0 + 0.1Mt. for some parameter 1. Write

Question:

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.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Question Posted: