Answer:
Answer explained below
Step-by-step explanation:
Spam e-mail containing a virus is sent to 1000 e-mail addresses. After 1 second, a recipient machine broadcasts 10 new spam e-mails containing the same virus, after which the virus disables itself on that machine. (1) Write a recursive definition (i.e. recurrence relation) to show how many spam emails will be sent out after n seconds. (2) Solve the recurrence relation. (3) How many e-mails are sent at the end of 20 seconds
1.START T=0.....
1000 EMAILS SENT AND RECEIVED BY 1000 M/CS.
T=1.....
EACH OF THE M/C SENDS 10 NEW MAILS ....
.................................
LET M[N] BE THE NUMBER OF MAILS SENT OUT AFTER N SECONDS.
SO , EACH OF THESE M/CS WILL SEND 10 MAILS IN NEXT 1 SECOND.
HENCE NUMBER OF MAILS SENT IN N+1 SECONDS=M[N+1]=
M[N+1]=10*M[N].......................1
THIS IS THE RECURRENCE RELATION.....
2.SOLUTION .....
M[N+1]=10M[N]=10*10M[N-1]=10*10*10M[N-2]=........
M(N+1)=[10^1][M(N)]=[10^2][M(N-1)]=[10^3][M(N-2)]=..........=[10^N][M(1)]=[10^(N+1)][M(0)]
M[N+1]=[10^(N+1)][1000]=[10^(N+1)][10^3]=[10^(N+4)]......................................2
THIS IS THE NUMBER OF MAILS SENT AFTER N+1 SECONDS .....OR ....
M[N]=[10^(N+3)].............................................3
..................IS THE SOLUTION FOR NUMBER OF MAILS SENT AFTER N SECONDS.....
3.AFTER N=20 SECONDS , THE ANSWER IS ....
M[20]=10^(20+3)=10^23
