document.write( "Question 451673: The half-life of a radioactive element is 131days, but your sample will not be useful to you after 70% of the radioactive nuclei originally present have disintegrated. About how many days can you use the sample? \n" ); document.write( "

Algebra.Com's Answer #310645 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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The half-life of a radioactive element is 131 days, but your sample will not be
\n" ); document.write( " useful to you after 70% of the radioactive nuclei originally present have disintegrated.
\n" ); document.write( " About how many days can you use the sample?
\n" ); document.write( ":
\n" ); document.write( "The radioactive decay equation: A = Ao*2^(-t/h), where
\n" ); document.write( "A = resulting amt in t time
\n" ); document.write( "Ao = initial amt
\n" ); document.write( "t = time
\n" ); document.write( "h = half-life of substance
\n" ); document.write( ":
\n" ); document.write( "Let Ao = 1
\n" ); document.write( "the
\n" ); document.write( "A = .3 after 131 days (70% decayed)
\n" ); document.write( ":
\n" ); document.write( "1*2^(-t/131) = .3
\n" ); document.write( "ln(2^(-t/131)) = ln(.3)
\n" ); document.write( "log equiv of exponents
\n" ); document.write( " $\"-t%2F131%29\"$ *ln(2) = ln(.3)
\n" ); document.write( " $\"-t%2F131%29\"$ = $\"ln%28.3%29%2Fln%282%29\"$
\n" ); document.write( " $\"-t%2F131%29\"$ = -1.7369656
\n" ); document.write( "t = -1.7369656 *-131
\n" ); document.write( "t = +227.5 days, the substance is useful
\n" ); document.write( ":
\n" ); document.write( ";
\n" ); document.write( "Check on a calc: enter 2^(-227.5/131) results .300
\n" ); document.write( " \n" ); document.write( "

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