SOLUTION: The half-life of radioactive strontium-90 is approximately 29 years. In 1964, radioactive strontium-90 was released into the atmosphere during testing of nuclear weapons, and was a

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Question 646647: The half-life of radioactive strontium-90 is approximately 29 years. In 1964, radioactive strontium-90 was released into the atmosphere during testing of nuclear weapons, and was absorbed into people's bones. How many years (since 1964) does it take until only 9 percent of the original amount absorbed remains?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The half-life of radioactive strontium-90 is approximately 29 years.
In 1964, radioactive strontium-90 was released into the atmosphere during
testing of nuclear weapons, and was absorbed into people's bones.
How many years (since 1964) does it take until only 9 percent of the
original amount absorbed remains?
:
The radio-active decay formula: A = Ao*2^(-t/h), where
A = resulting amt after t time
Ao = initial amt (t=0)
t = time of decay
h = half-life of substance
:
Let initial amt = 100 then resulting amt = 9
100*2^(-t/29) = 9
divide both sides by 100
2^(-t/29) = .09
using nat logs, the log equiv of exponents
-t%2F29*ln(2) = ln(.09)
-t%2F29 = ln.09%2Fln%282%29
-t%2F29 = -3.47393
t = -29 * -3.47393
t = 100.744 yrs, plus 1964 = 2065 for bones to be reduced to 9%
:
:
:
That seemed like a long time, checked on a calc:
enter 100*2^(-100.744/29) results: 9.000