Exponential dsn. please check my work

1. Nov 22, 2011

Bachelier

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?

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 = 1020* e-ln 2 t. ln 2 is my parameter since half time is 1 century.

thus t = ln(1020/ln 5) * (ln 2)-1 ≈ 65 years

2. Nov 23, 2011

mathman

Your time unit is centuries, not years. So your answer (I didn't check arithmetic) is 65 centuries.

3. Nov 23, 2011

Bachelier

what about the theory, is it correct?

4. Nov 24, 2011

mathman

Above has error, μ = -ln.5 = ln2

The general idea is correct. You might try a binomial to check. The result should be about the same.