Question 37085
The solution that I have obtained is not exact. 

Let f(a)=2^(2a)+5^a This equation will give you the number of infected computers, I will explain you how it works above.

The time will be equal to five times a

for example 

f(1)=20  computers infected in 1(5)=5 minutes
f(2)=400 computers infected in 2(5)=10 minutes
etc

the solution for 100 million computers is not exact you must use logartithms

Solution:

a= 8/(2log(2)+log(5))   log in decimal base

t= 5a the time is 5 times a
the time is aproximately 30.74487147 minutes

If you have any comment about the solution write me.