document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=590776>Question 590776</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A radioactive substance has a decay rate of 1.8% per year. What is its half life? Give your answer correct to 2 decimal places.\r<BR>\n" );
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document.write( "The radioactive element carbon-14 has a half-life of 5750 years. The percentage of carbon-14 present in the remains of plants and animals can be used to determine age. How old is a skeleton that has lost 44% of its carbon-14? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #375342 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=375342\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A radioactive substance has a decay rate of 1.8% per year.<BR>\n" );
document.write( " What is its half life? Give your answer correct to 2 decimal places.<BR>\n" );
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document.write( "The radioactive decay formula: A = Ao*2^(-t/h), where<BR>\n" );
document.write( "A = amt remaining after t time<BR>\n" );
document.write( "Ao = initial amt; t-0<BR>\n" );
document.write( "t = time of decay<BR>\n" );
document.write( "h = half-life of substance<BR>\n" );
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document.write( "let initial amt = 1<BR>\n" );
document.write( "then remaining amt = .982<BR>\n" );
document.write( "let t = 1 yr<BR>\n" );
document.write( "find h<BR>\n" );
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document.write( "1*2^(-1/h} = .982<BR>\n" );
document.write( "Use natural logs<BR>\n" );
document.write( "ln(2^(-1/h)) = ln(.982)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2Fh ALIGN=MIDDLE  ALT=\"-1%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28.982%29%2Fln%282%29 ALIGN=MIDDLE  ALT=\"ln%28.982%29%2Fln%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "use your calc<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2Fh ALIGN=MIDDLE  ALT=\"-1%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -.0262<BR>\n" );
document.write( "-.0262h = -1<BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F.0262 ALIGN=MIDDLE  ALT=\"1%2F.0262\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "h ~ 38.17 yrs is the half-life<BR>\n" );
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document.write( "The radioactive element carbon-14 has a half-life of 5750 years.<BR>\n" );
document.write( " The percentage of carbon-14 present in the remains of plants and animals can be used to determine age.<BR>\n" );
document.write( " How old is a skeleton that has lost 44% of its carbon-14?<BR>\n" );
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document.write( "Find the remaining carbon if initial amt = 1: 1-.44 = .66<BR>\n" );
document.write( "Find t<BR>\n" );
document.write( "1*2^(-t/5750} = .66<BR>\n" );
document.write( "Use natural logs<BR>\n" );
document.write( "ln(2^(-t/5750)) = ln(.66)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t%2F5750 ALIGN=MIDDLE  ALT=\"-t%2F5750\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28.66%29%2Fln%282%29 ALIGN=MIDDLE  ALT=\"ln%28.66%29%2Fln%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "use your calc<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t%2F5750 ALIGN=MIDDLE  ALT=\"-t%2F5750\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -.59946<BR>\n" );
document.write( "t = -5750 * -.59946<BR>\n" );
document.write( "t = +3,447 years<BR>\n" );
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