I just did the math in two ways: if each person infects 5 people who have never been infected, it only takes a bit more than 14 cycles from “patient zero” (whoever that was) to infect the entire living human population.
Obviously the real progress of an epidemic isn’t that simple.
Being a retired math teacher I figured this was a perfect case for using logarithms, so I did. (For me, that’s fun!) I went like this:
I’m trying to find n such that five to the nth power equals 7.5 billion, or in math-lingo,
5^n = 7.5*10^9
One takes the logarithms of both sides, and because of the wonderful properties of logs, I get n*log(5)=9+log(7.5) which we can solve for n by dividing both sides by log(5), obtaining
n = (9+log(7.5))/log(5), after which my calculator said n was about 14.1.
But if you have a cell phone you can confirm my result much more easily by asking it work out 5^14. I think you’ll find it’s about six billion; if you try 5^15 you’ll get an enormous umber, over 30 billion, which is much too high. We have only roughly seven and a half billion humans…