Question 187706: 7. 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?
I am dumbfounded by this and need explanation. I need to see the work here. thank you.
Answer by stanbon(75887)   (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 servers each infect 20 more machines within another five minutes, etc. How long until 100 million computers are infected?
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When you have a problem like this you should construct a table of pairs of
points; then try to see a pattern.
0,1
That 1 gets multiplied by 20 after 5 seconds
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5,1+20
That 1+20 gets multiplied by 20 after another 5 seconds
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10,(1+20)*20
Muliplied by 20 again
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15,[(1+20)*20]*20 = [(1+20)]*20^2
20,[(1+20)]*20^3
25,[(1+20)]*20^(25/5)-1)
30,[(1+20)]*20^((30/5)-1)
...
t seconds , [(1+20)]*20^((t/5)-1)
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Equation:
A(t) = (1+20)*20^((t/5)-1)
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How long until 100 million computers are infected?
Solve for t in seconds: (1+20)*20^((t/5)-1) = 100 million
20^((t/5)-1)] = (100/21) million
Take the log of both sides to get:
((t/5)-1)log(20) = log(100 million) - log(21)
((t/5)-1)log(20) = 8 - 1.3222 = 6.6778
[(t/5)-1] = 6.6778/1.3010 = 5.1327
(t/5) = 6.1327
t = 30.6635 seconds
or
time = 30.6635/60 = 0.5111 minutes
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Comment: I checked this out. You actually get 100,003,673 infected computers.
The additional 3673 computers is there because we are rounding off the
numbers as we do the calculations.
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Cheers,
Stan H.
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