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

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) (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:

We want to find X such that Y is equal to 100,000,000:

Applying natural logarithm:

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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