SOLUTION: The half-life of a certain element is two years. If the element has one isotope now, how old is it if it started with 8589734592 isotopes?

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Question 1119827: The half-life of a certain element is two years. If the element has one isotope now, how old is it if it started with 8589734592 isotopes?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The half-life of a certain element is two years.
If the element has one isotope now, how old is it if it started with 8589734592 isotopes?
:
Using the decay formula Ao*2^(-t/h) = A, where:
A = resulting amt after t time
Ao = Initial amt
t = time of decay
h = half-life of substance
:
8589734592*2^(-t/2) = 1
:
2%5E%28-t%2F2%29+=+1%2F8589734592
-t%2F2 ln(2) = ln%281%2F8589734592%29
-t%2F2 * .693 = -22.874
-t%2F2 = -22.874%2F.693
-t%2F2 = -33
t = -2 * -33
t = 66 yrs