SOLUTION: this is probably really simple but if you could help me it would be greatly appreciated You never believed in vampires , until you saw one for yourself. up until now he seems to

Question 873683: this is probably really simple but if you could help me it would be greatly appreciated
You never believed in vampires , until you saw one for yourself. up until now he seems to have been living off stray puppies in the neighborhood. According to your friend, vampires only come out at night and they only feed two times a month. Feeding means sucking the blood of a human, and after they�re through, that person becomes a vampire, too. One month later, these new vampires will each be capable of turning 2 more people into vampires.
your friend explains. �At the next full moon, he�ll be looking for human blood. The good news is that there�s only one vampire in town.�There are 500,000 people living in this town, right? That means, unless we find the vampire before the next full moon, our town will soon be completely taken over by vampires!� Your friend doesn't believe you, so you have to prove it to him.
If the vampires feed only on people in your town, approximately how many months will it take for your 500,000-person town to become populated entirely by vampires?
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
Start with one
1) mid month 2 there will be 4 at the end of the first month 2^2
2) then 8 2^3 mid 2nd month 16 end of 2nd month 2^4
3) 32 2^5 then 64 2^6
4) 128 2^7 then 256 2^8
5) 512 2^9 1024 2^10
6) 2048 2^11 4096 2^12
2^18=262144 ie 9th month so sometime in the 10 month it will reach 500000
see the pattern?
2^(2m)
500000<=2^(2m)

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