hw9-11 - AMS 301 (Fall, 2009) Estie Arkin Homework Set # 9...

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AMS 301 (Fall, 2009) Estie Arkin Homework Set # 9 Due in class on Monday, November 23, 2009. Recommended Reading: Tucker, 6.1, 6.2 2(b,c), 4(c), 14 — Section 6.1 4, 20 — Section 6.2 Homework Set # 10 Due in class on Wednesday, December 2, 2009. Recommended Reading: Tucker, 7.1, 7.2 6(a,b), 24 — Section 7.1 Problem A: A computer virus is spread by way of e-mail messages, and is planted in 3 machines the ±rst day. Each day, each infected machine from the day before infects 5 new machines. Let a n be the total number of machines that are infected (have this virus) on the n th day. (a). Write a recurrence for a n . Do not forget the complete set of initial conditions! (You do not have to solve the recurrence.) (b). Now suppose that on the second day a software solution is found to counteract the virus, and one machine is cleaned on this (the second) day. Each day thereafter, twice as many machines are cleaned as were cleaned the day before. Write a recurrence for a n . Do not forget the complete set of initial conditions!
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