SOLUTION: The half-life of 234U, uranium-234, is 2.52 105 yr. If 98.2% of the uranium in the original sample is present, what length of time (to the nearest thousand years) has elapsed? ex

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: The half-life of 234U, uranium-234, is 2.52 105 yr. If 98.2% of the uranium in the original sample is present, what length of time (to the nearest thousand years) has elapsed? ex      Log On


   

Question 519070: The half-life of 234U, uranium-234, is 2.52 105 yr. If 98.2% of the uranium in the original sample is present, what length of time (to the nearest thousand years) has elapsed?
explain in deatil how to get this solved?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
I think you mean
The half-life of 234U, uranium-234, is 2.52(10^5) yrs.
:
If 98.2% of the uranium in the original sample is present, what length of time (to the nearest thousand years) has elapsed?
:
The half-life formula: A = Ao*2(-t/h)
where:
A = resulting amt after t yrs
Ao = initial amt
h = half-life of substance
t = time of decay
:
Let initial amt; Ao = 100
A = 98.2, resulting amt
h = 2.52(10^5) yrs
find t
:
100*2^(-t/(2.52(10^5)) = 98.2
:
2^-t%2F2.52%2810%5E5%29 = 98.2%2F100
:
2^-t%2F2.52%2810%5E5%29 = .982
:
-t%2F2.52%2810%5E5%29*ln(2) = ln(.982)
:
-t%2F2.52%2810%5E5%29 = ln%28.982%29%2Fln%282%29
:
-t%2F2.52%2810%5E5%29 = -.0262
:
t+=+-.0262%2A-2.52%2810%5E5%29
t = 6,603.68 yrs