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## Main Question or Discussion Point

A piece of rock contains 10^20 atoms of a particular substance. Each atom has an expoentially distributed lifetime with a half-life of one century. How many centurites must pass before

there is about a 50% chance that at least one atom remains. What assumptions are you making?

answer:

so P (at least one survives past t) = P (no one does) = .5

now, I'm making the assumption that Prob of survival is so small and since n is huge, this follows a poisson disn.

thus .5 = P(k=0) = e

then μ = ln 5

now μ = np = 10

thus t = ln(10

there is about a 50% chance that at least one atom remains. What assumptions are you making?

answer:

so P (at least one survives past t) = P (no one does) = .5

now, I'm making the assumption that Prob of survival is so small and since n is huge, this follows a poisson disn.

thus .5 = P(k=0) = e

^{-μ}then μ = ln 5

now μ = np = 10

^{20}* e^{-ln 2 t}. ln 2 is my parameter since half time is 1 century.thus t = ln(10

^{20}/ln 5) * (ln 2)^{-1}≈ 65 years