For those who hate math, consider that University of Central Florida physics professor Costas Efthimiou used it to prove that Vampires can’t exist. In other words, not only does math not suck, nothing else does either.
Because there's a little cogitator in all of us...
If no vampires are ever killed, I can see how the geometric progression would extinguish the human population as posited.
I can’t remember my mythology – are vampires like werewolves in the sense that if you kill one those they have cursed are freed as long as they have not bitten someone else?
If there is a check and balance I would expect the population of vampires to ebb and flow much like any other “balance of nature” phenomenon.
I guess that also supposes that vampires are part of our natural world, bound by our natural laws, what dinnertime conversation.