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 email 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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 Spring '08
 ARKIN
 Recursion, Tucker

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