Assignment 1

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

This preview shows page 1. Sign up to view the full content.

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
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## 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.

Ask a homework question - tutors are online