document.write( "Question 571607: A substance has a half life of 23 hours .How old is the object that has 5% of the substance left? \r
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Algebra.Com's Answer #368157 by ankor@dixie-net.com(22740)![]() ![]() You can put this solution on YOUR website! A substance has a half life of 23 hours . \n" ); document.write( "How old is the object that has 5% of the substance left? \n" ); document.write( ": \n" ); document.write( "The radioactive decay formula: \n" ); document.write( "A = Ao*2^(-t/h), where \n" ); document.write( "A = resulting amt after t \n" ); document.write( "Ao = initial amt (t-0) \n" ); document.write( "t = time of decay \n" ); document.write( "h = half-life of substance \n" ); document.write( ": \n" ); document.write( "Let initial amt = 1, then we can write the equation \n" ); document.write( "1*2^(-t/23) = .05 \n" ); document.write( "Using nat logs and the log equiv of exponents \n" ); document.write( " \n" ); document.write( ": \n" ); document.write( " \n" ); document.write( "multiply both sides by -23 \n" ); document.write( ": \n" ); document.write( ": \n" ); document.write( "You can check this on a good calc: enter: 2^(-99.4/23), results: .05 which is 5% \n" ); document.write( "t = 99.4 days to a 5% remaining \n" ); document.write( " |