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September 22, 2014

September 22, 2014

Posted by **Annie** on Wednesday, September 19, 2012 at 3:46pm.

- Math -
**Steve**, Wednesday, September 19, 2012 at 4:43pmSince 1/8 = (1/2)^3, it will take 3 half-lives, or 96 years.

- Math -
**Reiny**, Wednesday, September 19, 2012 at 5:03pmI would say

.08 = (1/2)^(t/32)

ln .08 = (t/32) ln .5

t/32 = ln .08/ln .5 = 3.6438..

t = 116.6 years

rough check:

after 32 years --- 50% left

after 64 years --- 25% left

after 96 years --- 12.5% left , (which is 1/8 but not 8%)

after about 16 more years we would lose about 1/4 of what was left, leaving appr 3/4 of 12.5 or appr 9%

answer is quite plausible

- math - oops -
**Steve**, Wednesday, September 19, 2012 at 5:34pmouch. How did I read 8% as 1/8?

As usual, go with Reiny's answer!

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