document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1002742>Question 1002742</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 6.An anthropologist finds bone that her instruments measure it as  0.177% of the amount of Carbon-14 the bones would have contained when the person was alive. How long ago did the person die?<BR>\n" );
document.write( "The half life of carbon 14 is 5,730 years. Round your answer to the nearest thousand. <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 #619598 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=619598\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P = orginal amount of carbon 14 t years ago (right when the person died)<BR>\n" );
document.write( "A = current amount of carbon 14\r<BR>\n" );
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document.write( "Since \"An anthropologist finds bone that her instruments measure it as 0.177% of the amount of Carbon-14 the bones would have contained when the person was alive\" we know that A = 0.00177P because 0.177% = 0.00177\r<BR>\n" );
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document.write( "The half-life formula in this case is A = P*(1/2)^(t/5730)\r<BR>\n" );
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document.write( "A = P*(1/2)^(t/5730)\r<BR>\n" );
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document.write( "0.00177P = P*(1/2)^(t/5730) <font color=blue>Plug in A = 0.00177P</font>\r<BR>\n" );
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document.write( "0.00177 = (1/2)^(t/5730) <font color=blue>Divide both sides by P</font>\r<BR>\n" );
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document.write( "Ln(0.00177) = Ln((1/2)^(t/5730)) <font color=blue>Apply natural logs to both sides</font>\r<BR>\n" );
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document.write( "Ln(0.00177) = (t/5730)*Ln(1/2) <font color=blue>Use the rule Ln(x^y) = y*Ln(x)</font>\r<BR>\n" );
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document.write( "Ln(0.00177)/Ln(1/2) = t/5730 <font color=blue>Divide both sides by Ln(1/2)</font>\r<BR>\n" );
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document.write( "5730*Ln(0.00177)/Ln(1/2) = t <font color=blue>Multiply both sides by 5730</font>\r<BR>\n" );
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document.write( "t = 5730*Ln(0.00177)/Ln(1/2) <font color=blue>Flip the equation (a = b is the same as b = a)</font>\r<BR>\n" );
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document.write( "t = 52,383.8601165473 <font color=blue>Use a calculator</font>\r<BR>\n" );
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document.write( "t = 52,383.860  <font color=blue> Rounding to the nearest thousand (3 decimal places)</font>\r<BR>\n" );
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document.write( "The person died approximately <font size = 5 color=red>52,383.860</font> years ago </SPAN>\n" );
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