document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1150245>Question 1150245</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Iodine 131, which is produced by nuclear explosions, has a half-life of 8 days. In the spring of 1986, a nuclear explosion occurred at a nuclear power plant in Chernobyl, near Kiev in the Soviet Union. Suppose that the hay from nearby farms was contaminated by the fallout and could not be fed to dairy cows, since the iodine 131 would contaminate their milk. The hay was found to contain six times the allowable level of iodine 131 shortly after the explosion. How long must the hay be stored to be certain that the amount of iodine 131 is reduced to an acceptable level?\r<BR>\n" );
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document.write( "Use A = A0 ekt<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #771627 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=771627\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A=Aoe^(kt)<BR>\n" );
document.write( "find k with half-life of 8 days, so A=0.5 Ao<BR>\n" );
document.write( "0.5Ao=Aoe^8k<BR>\n" );
document.write( "0.5=e^8k<BR>\n" );
document.write( "ln both sides<BR>\n" );
document.write( "-0.693=8k<BR>\n" );
document.write( "k=-0.0866\r<BR>\n" );
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document.write( "Ao=6*A<BR>\n" );
document.write( "so this becomes<BR>\n" );
document.write( "ln(1/6)=e^(-0.0866t)<BR>\n" );
document.write( "-1.7918=-0.0866t<BR>\n" );
document.write( "t=-20.68 days if I round at the very end\r<BR>\n" );
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document.write( "This is about 2.5 half-lives, and 1/2.5^2 is 1/6.25 or about 1/6 as a rough check.<BR>\n" );
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