document.write( "Question 133943: How long does it take 12 grams of carbon-14 to decay to 10 grams when the decay is exponential with an annual rate of decay of 0.0124%? \n" ); document.write( "

Algebra.Com's Answer #98034 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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How long does it take 12 grams of carbon-14 to decay to 10 grams when the decay is exponential with an annual rate of decay of 0.0124%?
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\n" ); document.write( "Using the decay equation:
\n" ); document.write( "12 * (1-.000124)^t = 10
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\n" ); document.write( ".999876^t = $\"10%2F12\"$
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\n" ); document.write( "log(.999876^t) = log( $\"10%2F12\"$ ); divided both sides by 12, using logs
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\n" ); document.write( "t*log(.999876) = log( $\"10%2F12\"$ ); using log equiv of exponents
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\n" ); document.write( "-.00005385t = -.07918; find the actual logs
\n" ); document.write( "t = $\"%28-.07918%29%2F%28-.00005385%29\"$
\n" ); document.write( "t = 1,470 years
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\n" ); document.write( "Check on a calc, enter: 12(1-.000124)^1470 = 10.000 \n" ); document.write( "

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