document.write( "Question 163533: can someone please help me with this problem:\r
\n" ); document.write( "\n" ); document.write( "A certain radioactive isotope decays at a rate of 0.25% annually. Determine the half - life of this isotope, to the nearest year.\r
\n" ); document.write( "\n" ); document.write( "a. 120 years
\n" ); document.write( "b. 277 years
\n" ); document.write( "c. 200 years
\n" ); document.write( "d. 3 years
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Algebra.Com's Answer #120479 by Fombitz(32388)\"\" \"About 
You can put this solution on YOUR website!
The isotope follows this power law as a function of time,
\n" ); document.write( "\"N%28t%29=N%5B0%5D%28.9975%29%5Et\"
\n" ); document.write( "where t is measured in years and \"N%5B0%5D\" is the initial amount of the isotope.
\n" ); document.write( "Half life is when \"N%28t%29=%281%2F2%29N%5B0%5D\",
\n" ); document.write( "\"%281%2F2%29N%5B0%5D=N%5B0%5D%280.9975%29%5Et\"
\n" ); document.write( "\"%280.5%29=%280.9975%29%5Et\"
\n" ); document.write( "\"t=log%280.9975%2C0.5%29\"
\n" ); document.write( "\"t=276.9\"
\n" ); document.write( ".
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\n" ); document.write( "Looks like b) 277 years is the closest answer.
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