Help ME With Math?

Question

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 1

Ok, so every 5 minutes, 20 computers are infected. So it can be determined that 4 computers are infected per minute. [20 divided by 5]. So to figure out how long it takes 100 million computers to be infected, you just have to plug in the numbers. So you have to divide 100,000,000 by 4 to get your answer. Sorry, I don't have a calculator on me... but I believe it's going to be about 25,000,000.... but I'd still check with a calculator.

I hope I helped. =]

Answer 2

You don't specify whether an infected computer infects 20 more computers every five minutes, or just infects 20 in the first five minutes, then stops. I'll assume the latter.

If t = 0 is the starting time, and one unit of time is five minutes long, then

At time t = 0, there is 1 computer infected.
At time t = 1, there are 1 + 20 computers infected.
At time t = 2, there are 1 + 20 + 20^2 computers infected.
At time t = 3, there are 1 + 20 + 20^2 + 20^3 computers infected
And so on.

The formula that describes how many computers are infected after a given number of five-minute time periods is:

F(t) = Sum(20^i, 0, t)

which is read as "the Riemann sum of 20^i, iterating i from 0 to t".

Here are the first few values of the formula:
When t = 0, F(t) = 1
When t = 1, F(t) = 21
When t = 2, F(t) = 421
When t = 3, F(t) = 8,421
When t = 4, F(t) = 168,421
When t = 5, F(t) = 3,368,421
When t = 6, F(t) = 67,368,421
When t = 7, F(t) = 1,347,368,421

So, 100,000,000 computers will be infected somewhere between t = 6 and t = 7. That is, somewhere between 30 and 35 minutes after the initial infection.