Assignment 1 - t = 20 (starting from M = 16) (f) Find the...

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MAT 1330 3X Assignment 1 Due date: May, 17, 2011 Total: 10 points Problem 1. (1.5.8) [ 7 points ] Each day, a patient uses up 75% of the medication in his bloodstream. However, he is given a new dose sufficient to raise the concentration in his bloodstream by 2.0 milligrams per liter. Let M t denote the concentration at time t . (a) Write the associated discrete time dynamical system and identify the updating function (b) Compose with itself the updating function and find the two step discrete time dynam- ical system (c) Find the backwards discrete time dynamical system and use it to find the value at the previous time, knowing that M 1 = 16 (d) Find and graph the first five values of the discrete time dynamical system, starting from M 0 = 16 (e) Find the solution, algebraically and use the formula to find the concentration at
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Unformatted text preview: t = 20 (starting from M = 16) (f) Find the equilibrium point (g) Cobweb for three steps, starting from M = 16. Problem 2. (1.6.34) [ 2 points ] Find the equilibria of the following discrete time dynamical system that includes the parameter K: x t +1 = x t x t-K . Identify values of the parameter for which there is a single equilibrium, for which the equilib-rium is negative, and for which there is more than one equilibrium. Problem 3. (1.8.52) [ 1 point ] Sleepiness has two cycles a circadian rhythm and an ul-tradian rhythm. The ultradian rhythm has a period of approximately four hours, phase 0, average 0 and the amplitude is 0.4 sleepiness unit. Find the formula and sketch the graph of sleepiness over the course of a day due to the ultradian rhythm. 1...
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This note was uploaded on 12/19/2011 for the course MAT 1330 taught by Professor Dumitriscu during the Fall '08 term at University of Ottawa.

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