document.write( "Question 155032: The level of thorium in a sample decreases by a factor of one-half every 4.2 million years. A meteorite is discovered to have only 7.6% of it's original thorium remaining. How old is the meteorite? \n" ); document.write( "
Algebra.Com's Answer #114158 by ankor@dixie-net.com(22740)\"\" \"About 
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The level of thorium in a sample decreases by a factor of one-half every 4.2 million years. A meteorite is discovered to have only 7.6% of it's original thorium remaining. How old is the meteorite?
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\n" ); document.write( "The half-life formula:
\n" ); document.write( "A = Ao*2^(-t/h)
\n" ); document.write( "where:
\n" ); document.write( "Ao = initial amt (= 1 in this problem)
\n" ); document.write( "A = resulting amt (decimal equiv of %)
\n" ); document.write( "t = time (in millions of years here)
\n" ); document.write( "h = half-life of the substance (millions of years)
\n" ); document.write( ":
\n" ); document.write( ".076 = 1*2^(-t/4.2)
\n" ); document.write( "or
\n" ); document.write( "2^(-t/4.2) = .076
\n" ); document.write( ":
\n" ); document.write( "Find the nat log of both sides:
\n" ); document.write( "\"%28-t%2F4.2%29\"*.693147 = -2.577022
\n" ); document.write( ":
\n" ); document.write( "\"-t%2F4.2\" = \"-2.577022%2F.693147\"
\n" ); document.write( "Cross multiply:
\n" ); document.write( "-.693147t = 4.2 * -2.577022
\n" ); document.write( ":
\n" ); document.write( "-.693147t = -10.8235
\n" ); document.write( "t = \"10.8235%2F.693147\"; (minus into a minus is plus)
\n" ); document.write( "t = 15.615 million years old
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\n" ); document.write( ":
\n" ); document.write( "Check solution on a calc: enter 2^(-15.615/4.2) = .075999 ~ .076 or 7.6%
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