document.write( "Question 676393: The half-life of 234U, uranium-234, is 2.52 105 yr. If 97.6% of the uranium in the original sample is present, what length of time (to the nearest thousand years) has elapsed? I got the 97.9 = 8000 but having trouble working thru this one. thanks \n" ); document.write( "

Algebra.Com's Answer #420346 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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The half-life of 234U, uranium-234, is 2.52(10^5) yr.
\n" ); document.write( "If 97.6% of the uranium in the original sample is present, what length of time (to the nearest thousand years) has elapsed?
\n" ); document.write( ":
\n" ); document.write( "The radioactive decay formula: A =Ao*2(-t/h), where:
\n" ); document.write( "A = Amt after t time
\n" ); document.write( "Ao = initial amt (t=0)
\n" ); document.write( "h = half-life of substance
\n" ); document.write( "t = time of decay
\n" ); document.write( ":
\n" ); document.write( "Assume the initial amt is 1
\n" ); document.write( "1*2^(-t/(2.52(10^5)) = .976
\n" ); document.write( "using nat logs
\n" ); document.write( " $\"-t%2F2.52%2810%5E5%29\"$ *ln(2) = ln(.976)
\n" ); document.write( ":
\n" ); document.write( " $\"-t%2F2.52%2810%5E5%29\"$ = $\"ln%28.976%29%2Fln%282%29\"$
\n" ); document.write( ":
\n" ); document.write( " $\"-t%2F2.52%2810%5E5%29\"$ = -.035047
\n" ); document.write( "t = -2.52(10^5) * -.035047
\n" ); document.write( "t = 8832 ~ 9,000 yrs \n" ); document.write( "

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