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.