document.write( "Question 1199238: The half-life of Radium 266 is 1590 years how many years does it take for 100mg of Radium 266 to decay to a mass of 70mg? \n" ); document.write( "

Algebra.Com's Answer #833011 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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The half-life of Radium 266 is 1590 years
\n" ); document.write( " how many years does it take for 100mg of Radium 266 to decay to a mass of 70mg?
\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 years
\n" ); document.write( "Ao = initial amt
\n" ); document.write( "t = time of decay
\n" ); document.write( "h = half-life of substance
\n" ); document.write( ":
\n" ); document.write( "In this problem we can write it
\n" ); document.write( "100*2^(-t/1590) = 70
\n" ); document.write( "2^(-t/1590) = $\"70%2F100\"$
\n" ); document.write( "2^(-t/1590) = .7
\n" ); document.write( "using nat logs $\"%28-t%2F1590%29%2Aln%282%29+=+ln%28.7%29\"$
\n" ); document.write( "ln(2^(-7/1590)) = ln(.7)
\n" ); document.write( "log equiv of exponents
\n" ); document.write( " $\"%28-t%2F1590%29%2Aln%282%29+=+ln%28.7%29\"$
\n" ); document.write( " $\"%28-t%2F1590%29\"$ = $\"ln%28.7%29%2Fln%282%29\"$
\n" ); document.write( "calc
\n" ); document.write( " $\"-t%2F1590\"$ = -.51457
\n" ); document.write( "t = -1590 * -.51457
\n" ); document.write( "t = 818 years \n" ); document.write( "

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