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Assignment 1 - x = 1500(Four points are enough(f Draw the...

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MAT 1330, Fall 2010 Assignment 1 Due Wednesday September 29, 8:30am at the beginning of class. Late assignments will not be accepted; nor will unstapled assignments. Instructor (circle one): Frithjof Lutscher Angelika Welte Aziz Khanchi Robert Smith? DGD (circle one): 1 2 3 4 Student Name Student Number By signing below, you declare that this work was your own and that you have not copied from any other individual or other source. Signature 1. Suppose you deposit $1000 each week into a special savings account, but the bank takes 5% of the total in fees. A discrete-time system modelling your investment is x n +1 = 0 . 95 x n + 1000 . (a) If you initially have $1500 in the bank, how much money will you have after the third week? (b) Write down the updating function of the dynamical system. (c) Find all equilbrium points of the dynamical system. (d) Give the solution of the dynamical system with x 0 = 1500. (e) Draw the solution of the dynamical system with
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Unformatted text preview: x = 1500. (Four points are enough.) (f) Draw the cobweb diagram of the dynamical system with x = 1500. (Four iterations are enough.) (g) Determine the stability of the equilibrium point using the cobweb diagram. 2. A disease is spreading through campus. Each day, the number of people infected depends on how many were infected the day before, according to the formula y n +1 = 6 . 2976 y n 1 + 0 . 0112 y n . (a) If one person is initially infected, how many people are infected after the ±rst day? after the second day? after the third? (b) Find all equilibrium points of the dynamical system. (c) How many people would you guess will be infected eventually? 3. A city is growing at a rate of 1% per year and initially has 1,000,000 individuals. What will be the population in 50 years’ time? 1...
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