document.write( "Question 88634: If 40 mg of a radioactive substance decays to 5mg in 12 minutes, find the half-life, in minutes, of the substance. \n" ); document.write( "
Algebra.Com's Answer #64440 by ankor@dixie-net.com(22740)\"\" \"About 
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If 40 mg of a radioactive substance decays to 5mg in 12 minutes, find the half-life, in minutes, of the substance.
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\n" ); document.write( "The half life formula: A = Ao* 2^(-t/h)
\n" ); document.write( "Where:
\n" ); document.write( "A = Amt at time t
\n" ); document.write( "Ao - initial amt
\n" ); document.write( "h = half-life
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\n" ); document.write( "Substitute for A, Ao, and t to find h:
\n" ); document.write( "40*2^(-12/h) = 5
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\n" ); document.write( "2^(-12/h) = 5/40; divide both sides by 40
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\n" ); document.write( "ln(2^(-12/h)) = ln(5/40)
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\n" ); document.write( "(-12/h)* ln(2) = ln(5/40); log equivalent of exponents
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\n" ); document.write( "(-12/h)*.693147 = -2.07944
\n" ); document.write( "-12/h = -2.07944/.693147
\n" ); document.write( "-12/h = -3
\n" ); document.write( "-3h = -12
\n" ); document.write( "h = -12/-3
\n" ); document.write( "h = 4 minutes is the half life
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\n" ); document.write( "Check on a calc: 40*2^-12/4) = 5\r
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