# math

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A vampire could have the ability to infect an entire planet if he bit 2 people each day. Those 2 people would bite 2 people the next day, and then all of those vampires would each bite 2 people the next day, and so forth... How would I solve this to find out how many people would be infected in about a month? Is there an equation?

• math -

look at the pattern
day 1 -- 2
day 2 --- 4 = 2^2
day 3 -- 8 = 2^3
...

day 10 ---- 2^10
..
day 30 = 2^30 (huge)

number infected = 2 + 4 + 8 + ... + 2^10
this is a geometric series, with a = 2, r = 2
sum = a(r^n-1)/(r-1)
= 2(2^30 - 1)/ (2-1) = appr 2.14 billion

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