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

The half-life of radioactive strontium-90 is approximately 32 years. In 1961, radioactive strontium-90 was released into the atmosphere during testing of nuclear weapons, and was absorbed into people's bones. How many years does it take until only 8 percent of the original amount absorbed remains?

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

- Math -
**Reiny**, Wednesday, September 19, 2012 at 5:03pm
I 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 5:34pm
ouch. How did I read 8% as 1/8?

As usual, go with Reiny's answer!

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