SOLUTION: A computer is infected with the Sasser virus. Assume that it infects 20 other computers within 5 minutes; and that these PCs and servers each infect 20 more machines within another

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Question 200183: A computer is infected with the Sasser virus. Assume that it infects 20 other computers within 5 minutes; and that these PCs and servers each infect 20 more machines within another five minutes, etc. How long until 100 million computers are infected?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A computer is infected with the Sasser virus.
Assume that it infects 20 other computers within 5 minutes; and that these PCs
and servers each infect 20 more machines within another five minutes, etc.
How long until 100 million computers are infected?
;
Let t = no. of minutes for this to happen
100 million = 10^8
:
20^(t/5) = 10^8
;
t%2F5*log(20) = log(10^8)
Find the logs, use the log equiv of exponents
t%2F5*1.3 = 8
Multiply both sides by 5
1.3t = 8 * 5
1.3t = 40
t = 40%2F1.3
t ~ 30.77 minutes for a 100 million to infected
:
;
Check solution on calc: enter 20^(30.77/5) = 101,516,957 ~ 100 million