Problem A: A cemputer 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 an be the total number of machines that are infected (have this virus) on the nth day. (3). Write a recurrence for (in. 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 an. Do not forget the complete set of initial conditions! (You do not have to solve the recurrence.) Divide and Conquer Solutions Solutions to the recurrence an = can/k + f(n) are given by C f (n) an C = 1 d d [logk n] + A c = k d An - K-I dn Anlosk C+ K-C n C = k dn dn([logk n] + A)