document.write( "Question 913640: suppose a radioactive isotope is such that one-ninth of atoms in a sample decay after eight years. Find the half life of this isotope. Round to one decimal place. \n" ); document.write( "

Algebra.Com's Answer #554629 by josgarithmetic(39617) $\"\"$ $\"About$

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p, amount present at passage of time t, (years)
\n" ); document.write( "I, initial amount for any t=0
\n" ); document.write( "k, a constant
\n" ); document.write( " $\"p=Ie%5E%28kt%29\"$ , the general decay model\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "One-ninth after 8 years.
\n" ); document.write( " $\"1%2F9=1%2Ae%5E%28k%2A8%29\"$
\n" ); document.write( " $\"ln%281%2F9%29=ln%28e%5E%288k%29%29\"$
\n" ); document.write( " $\"8k%2Aln%28e%29=ln%281%2F9%29\"$
\n" ); document.write( " $\"k=%28ln%281%2F9%29%29%2F8\"$
\n" ); document.write( " $\"highlight_green%28k=-ln%289%29%2F8%29\"$
\n" ); document.write( " $\"highlight_green%28k=-0.2747%29\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The question was, find the half-life.
\n" ); document.write( " $\"Ie%5E%28-0.2747t%29=p\"$
\n" ); document.write( " $\"1%2Ae%5E%28-0.2747t%29=1%2F2\"$
\n" ); document.write( " $\"ln%28e%5E%28-0.2747t%29%29=ln%281%2F2%29\"$
\n" ); document.write( " $\"-0.2747t%2A1=ln%281%2F2%29\"$
\n" ); document.write( " $\"t=-ln%281%2F2%29%2F%280.2747%29\"$
\n" ); document.write( " $\"t=ln%282%29%2F0.2747\"$
\n" ); document.write( " $\"t=2.5233\"$ ----------- $\"highlight%28t=2.5%29\"$ when rounded to nearest tenth.
\n" ); document.write( "Rounded to ONE decimal place, 2.5 years, the half-life. \n" ); document.write( "

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