math modeling class

MATLAB EXCEPT PART B DO IT BY HAND

1) Consider the following model for a drug prescription:

An+1 = An kAn + b

(1) with An is the amount of drug (in mg) in the bloodstream after administration of n dosages at regular intervals (hourly).

(a) Discuss the meaning of the model parameters k and b. What can you say about their size and sign?

(b) Find the fixed points of the model and their stability via linearization. (Do this problem by hand and turn in a hard copy on paper showing your work) (

c) Perform a graphical analysis for this model by making a cobweb diagram. What happens to the amount of drug in the bloodstream in the long run? How does the result depend on the model parameters?

(d) How should b be chosen to ensure that the drug is effective, but not toxic?