document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199250>Question 1199250</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The half-life of a radioactive substance is one hundred twenty-five days. How many days will it take for eighty-two percent of the substance to decay?\r<BR>\n" );
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document.write( "A. 180<BR>\n" );
document.write( "B. 367<BR>\n" );
document.write( "C. 275<BR>\n" );
document.write( "D. 310<BR>\n" );
document.write( "E. 532<BR>\n" );
document.write( "F. 426 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833033 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=833033\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> half life is 125 days.<BR>\n" );
document.write( "formula becomes .5 = g ^ 125<BR>\n" );
document.write( "g is the growth rate per day.<BR>\n" );
document.write( "take the 125th root of both sides of the equation to get:<BR>\n" );
document.write( ".5 ^ (1/125) = g<BR>\n" );
document.write( "solve for g to get:<BR>\n" );
document.write( "g = .9944701687<BR>\n" );
document.write( "that's the daily growth rate.<BR>\n" );
document.write( "if the radioactive substance starts at 1 and you want 82% to decay, then the remainder would be 1 - .82 * 1 = .18.<BR>\n" );
document.write( "the formula decays from 1 to .18 in x days.<BR>\n" );
document.write( "the formula becomes .18 = 1 * .9944701687 ^ x<BR>\n" );
document.write( "simplify to get .18 = .9944701687 ^ x<BR>\n" );
document.write( "take the log of both sides of the equation to get:<BR>\n" );
document.write( "log(.18) = log(.9944701687 ^ x)<BR>\n" );
document.write( "this becomes log(.18) = x * log(.9944701687)<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = log(.18) / log(.9944701687) = 309.2413985 days.<BR>\n" );
document.write( "that's pretty close to 310, so selection D should be your answer.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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