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?
3 answers
Since 1/8 = (1/2)^3, it will take 3 half-lives, or 96 years.
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
.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
ouch. How did I read 8% as 1/8?
As usual, go with Reiny's answer!
As usual, go with Reiny's answer!
0 answers