document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1088848>Question 1088848</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An unknown radioactive element decays into non-radioactive substances. In 840 days the radioactivity of a sample decreases by 48 percent.\r<BR>\n" );
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document.write( "(a) What is the half-life of the element?\r<BR>\n" );
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document.write( "(b) How long will it take for a sample of 100 mg to decay to 69 mg?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #703164 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=703164\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The half-life formula is<BR>\n" );
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document.write( "N(t) = N(0) * (1/2)^(t/t(1/2))<BR>\n" );
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document.write( "solve for t(1/2)<BR>\n" );
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document.write( "1) t(1/2) = t / (log(1/2)(N(t)/N(0))<BR>\n" );
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document.write( "let N(0) = 1.0 and N(t) = (1.0 - 0.48) = 0.52 and t = 840<BR>\n" );
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document.write( "t(1/2) = 840 / (log(1/2) (0.52/1.0)) = 893.6 approx 894 days<BR>\n" );
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document.write( "a) half-life is 894 days<BR>\n" );
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document.write( "solve equation 1) for t<BR>\n" );
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document.write( "t = t(1/2) * (log(1/2)(N(t)/N(0))<BR>\n" );
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document.write( "t = 894 * log(1/2) (69/100) = 894 * 0.535 = 478.29 approx 478<BR>\n" );
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document.write( "b) it will take 478 days for sample to decay from 100 mg to 69 mg<BR>\n" );
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