math
posted by joe on .
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?

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^n1)/(r1)
= 2(2^30  1)/ (21) = appr 2.14 billion