1) I assume that you mean
When the sample is grown to 5,000,000,000 we have that:
Take the log of both sides:
We know that , so:
Just plug that into your calculator and you have your answer.
2) Yes that is correct.
3) Let's call the number of computers infected . We know that after 5 minutes, 20 computers are infected, plus the original 1. We also know that exponentials are of the form:
So we then have:
To find how long until 100,000,000 computers are infected, simply set the equation equal to 0 and solve for using the method from question 1.