A computer virus is spread by way of e-mail messages, and is planted in 3 machin

Question

A computer virus is spread by way of e-mail messages, and is planted in 3 machines the first 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 nth 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 (You do not have to solve the recurrence.)

Explanation / Answer

Let an be the no of machines infected on nth day

a1 = 3

New machines infected the next day = 5a1

Hence a2 = a1+5a1 = 6a1, a1 = 3

a2 = 18

a3 = a2+5a2 = 6a2=6(18)

and so on

an+1 = 6 an is the recurrence formula

an+1 = 6n a1 = 3(6n)

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b) a1 = 3

a2 = 6a1-1 = 17

a3 = 6a2-1 = 6(6a1-1)-1

and so on

an+1 = 6(an) -1 is the recurrence formula

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b)

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