SOLUTION: A computer is infected with the Boro 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 37108: A computer is infected with the Boro 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 mbarugel(146) About Me  (Show Source):
You can put this solution on YOUR website!
Hello!
Let's call X to the number of 5-minute blocks that have passed since the first computer was infected.
When X = 1 (5 minutes have passed), there are 20 infected computers
When X = 2 (10 minutes have passed), there are 20*20 = 20^2 infected computers
When X = 3 (15 minutes have passed), there are 20*20*20 = 20^3 infected computers
and so on...
So the formula for the number of infected computers is:
Y+=+20%5EX
We want to find X such that Y is equal to 100,000,000:
100000000+=+20%5EX
Applying natural logarithm:
ln%28100000000%29+=+X%2Aln%2820%29
X=ln%28100000000%29%2Fln%2820%29+=+6.1489
Therefore, there will be 100,000,000 infected computers after 6.1489 5-minute blocks, or 6.1489*5 = 30.74 minutes

I hope this helps!
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