document.write( "Question 822989: Find the half-life of a radioactive substance that decays by 2% in 9 years. \n" ); document.write( "

Algebra.Com's Answer #495227 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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Find the half-life of a radioactive substance that decays by 2% in 9 years.
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\n" ); document.write( "Using the radioactive decay formula; A = Ao*2^(-t/h), where:
\n" ); document.write( "A = amt remaining after t time
\n" ); document.write( "Ao = initital amt (t=0)
\n" ); document.write( "t = time of decay
\n" ); document.write( "h = half-life of substance
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\n" ); document.write( "Let initial amt = 1, then resulting amt after 9 yrs = .98 (2% less)
\n" ); document.write( "1*2^(-9/h) = .98
\n" ); document.write( "using nat logs
\n" ); document.write( " $\"-9%2Fh\"$ ln(2) = ln(.98)
\n" ); document.write( " $\"-9%2Fh\"$ = $\"ln%28.98%29%2Fln%282%29\"$
\n" ); document.write( " $\"-9%2Fh\"$ = -.029
\n" ); document.write( "h = $\"%28-9%29%2F%28-.029%29\"$
\n" ); document.write( "h = 309 yrs is the half life
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\n" ); document.write( "Check this on your calc; enter 1*2^(-9/309); results .98 or 98% remains \n" ); document.write( "

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