document.write( "Question 1191731: The half life of cobalt -60 is 5.27 years. Starting with a sample of 150 mg, after how many years is 20 mg left? \n" ); document.write( "

Algebra.Com's Answer #823548 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Both responses you have received show the same right answer; but the calculations performed in each response are far more convoluted than what is necessary.

\n" ); document.write( "You have 150mg of a substance decaying to 20mg in an unknown number of half-lives. The equation is simple:

\n" ); document.write( " $\"150%28%281%2F2%29%5En%29=20\"$
\n" ); document.write( " $\"150%2F20+=+2%5En\"$

\n" ); document.write( "The variable is in an exponent, so use logarithms and use a calculator.

\n" ); document.write( " $\"n%2Alog%282%29=log%287.5%29\"$
\n" ); document.write( " $\"n+=+log%287.5%29%2Flog%282%29\"$

\n" ); document.write( "That number of half-lives, to several decimal places, is 2.90689. Multiply that by the 5.27 years for one half life and you get the answer of approximately 15.32 years.

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\n" ); document.write( "It should be noted that radioactive decay is a statistical process; after one half life the amount remaining is APPROXIMATELY half of the original. So keeping 6 or 7 decimal places in the answer to a problem like this is unreasonable.

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