Question

Once a computer worm infects a personal computer via an infected e-mail message, it sends a copy of itself to 100 e-mail addresses it finds in the electronic message mailbox on this personal computer. What is the maximum number of different computers this one computer can infect in the time it takes for the infected message to be forwarded five times?

Answer 1

Answer: a maximum of 10,000,000,000 infected computers

Explanation:

when it is forwarded 1 time, it can infect a maximum of 100 computers.

now, the second time, each of these 100 computers can infect a maximum of 100 computers each, so we have 100*100 = 10,000 computers infected, and so on.

This is an exponential relation, that we can write as:

Infections(t) = 1*100^t

where 1 is the initial computer infected, (so when t = 0, we have only one computer infected)

The maximum number of computers infected can be finded if we took t = 5.

Infections(5) = 1*100^5 = 10,000,000,000

(this is a maximum number because we do not considerate the possibility that the virus goes back to computers that are already infected, if we considerate that probability we will have a smaller number)