document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=595563>Question 595563</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please show all work. Thanks in advance.\r<BR>\n" );
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document.write( "1. The half life of carbon14 is 5730 yrs. How long does it take for 2.8 grams of carbon 14 to be reduced to 1.1 grams ofcarbon-14 by radioactive decay? (Don't round to the final answer.)   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #377340 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=377340\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The half life of carbon14 is 5730 yrs.<BR>\n" );
document.write( " How long does it take for 2.8 grams of carbon 14 to be reduced to 1.1 grams ofcarbon-14 by radioactive decay?<BR>\n" );
document.write( " (Don't round to the final answer.)<BR>\n" );
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document.write( "The radioactive decay formula: A = Ao*2^(-t/h), where<BR>\n" );
document.write( "A = resulting amt after t time<BR>\n" );
document.write( "Ao = initial amt<BR>\n" );
document.write( "t = decay time<BR>\n" );
document.write( "h = half-life of substance<BR>\n" );
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document.write( "2.8*2^(-t/5730) = 1.1<BR>\n" );
document.write( "Divide both sides by 2.8<BR>\n" );
document.write( "2^(-t/5730) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.1%2F2.8 ALIGN=MIDDLE  ALT=\"1.1%2F2.8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2^(-t/5730) = .392857<BR>\n" );
document.write( "Using nat logs<BR>\n" );
document.write( "ln[2^(-t/5730)] = ln(.392857)<BR>\n" );
document.write( "log equiv of exponents<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t%2F5730 ALIGN=MIDDLE  ALT=\"-t%2F5730\"   DISABLED_style= \"max-width:90%; height:auto;\" >*ln(2) = ln(.392857)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t%2F5730 ALIGN=MIDDLE  ALT=\"-t%2F5730\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28.392857%29%2Fln%282%29 ALIGN=MIDDLE  ALT=\"ln%28.392857%29%2Fln%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "find the ln<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t%2F5730 ALIGN=MIDDLE  ALT=\"-t%2F5730\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -1.3479<BR>\n" );
document.write( "Multiply both sides by -5730<BR>\n" );
document.write( "t = -1.3479 * -5730<BR>\n" );
document.write( "t = 7,723.6 yrs to decay to 1.1 grams </SPAN>\n" );
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