document.write( "Question 1142059: The half-life of carbon 14 is 5,730 years. Approximately, how old is a bone that has 70% of its original carbon 14? \n" ); document.write( "

Algebra.Com's Answer #762710 by greenestamps(13203) $\"\"$ $\"About$

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\n" ); document.write( "The fraction remaining after n half-lives is $\"%281%2F2%29%5En\"$ .

\n" ); document.write( "You want to know when the fraction remaining is 70%, or .7.

\n" ); document.write( " $\"%281%2F2%29%5En+=+%28.5%29%5En+=+.7\"$

\n" ); document.write( "The variable is an exponent, so use logarithms:

\n" ); document.write( " $\"n%2Alog%28.5%29+=+log%28.7%29\"$
\n" ); document.write( " $\"n+=+log%28.7%29%2Flog%28.5%29\"$ = 0.514573 to 6 decimal places.

\n" ); document.write( "Then the age is the number of half-lives, multiplied by the number of half-lives.

\n" ); document.write( " $\"5730%2A0.514573+=+2948.5\"$

\n" ); document.write( "Since the problem says approximately, a good answer is 2950 years. \n" ); document.write( "

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