Doomsday

Algebra Level pending

As some people prophesied it, today marks the end of the world! A deadly virus has been released and contaminated on Day 1 one human being! On the second day, this person will contaminate on extra person. On the third day, both people will infect 2 other and different people. Suppose that, in general, on each subsequent day, every infected person will contaminate a person, which has not yet been contaminated (so, to avoid ambiguities, no 2 infected people can contaminate the same person). Supposing that the world population is at \(7 * 10^9\) individual on Day 1, and that the births following this day are negligible, find X such that Day X marks the very day when every human being is infected!

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