1. Consider the following situation: A patient starts with a concentration of medicine in his bloodstream...

 

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1. Consider the following situation: A patient starts with a concentration of medicine in his bloodstream equal to 10 milligrams per liter. Each day, the patient uses up 30% of the medication in his bloodstream. However, at the end of each day, he takes enough medication to increase the concentration of medication in the bloodstream by 5 milligrams per liter. (a) Write down a discrete-time dynamical system (updating function) and initial condition describing this situation. (Let Mi = the concentration of medicine in the bloodstream on day t.) (b) Iterate your DTDS to find the concentration of medicine in the bloodstream in days 1 through 7. Graph your values as a function of time t. (Don't forget to label the axes.) (e) Cobweb your discrete-time dynamical system, starting at Mo = 10, and labeling your axes and the first three iterations on the cobweb diagram. What is the long-term behavior of the system? (d) Find any equilibria for your discrete-time dynamical system algebraically. 1. Consider the following situation: A patient starts with a concentration of medicine in his bloodstream equal to 10 milligrams per liter. Each day, the patient uses up 30% of the medication in his bloodstream. However, at the end of each day, he takes enough medication to increase the concentration of medication in the bloodstream by 5 milligrams per liter. (a) Write down a discrete-time dynamical system (updating function) and initial condition describing this situation. (Let Mi = the concentration of medicine in the bloodstream on day t.) (b) Iterate your DTDS to find the concentration of medicine in the bloodstream in days 1 through 7. Graph your values as a function of time t. (Don't forget to label the axes.) (e) Cobweb your discrete-time dynamical system, starting at Mo = 10, and labeling your axes and the first three iterations on the cobweb diagram. What is the long-term behavior of the system? (d) Find any equilibria for your discrete-time dynamical system algebraically.

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a As initial concentration is 10 mgL Usage everyday 30 of present concentration Everyday increase 5 ... View the full answer