document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195957>Question 1195957</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi please assist me with this question\r<BR>\n" );
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document.write( "Radioactive carbon-14 is used to determine the age of artifacts because it concentrates in the <BR>\n" );
document.write( "organism only when they are alive. It has a half-life of 5730 years. In 1947, Dead Sea Scroll <BR>\n" );
document.write( "were found by one of the South Africa Universities professor. Analysis indicate that scroll<BR>\n" );
document.write( "wrapping contain s 76% of their original carbon -14. Estimate the age of the Dead Sea Scroll.<BR>\n" );
document.write( "[10 marks]<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 #828598 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=828598\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .5 = (1+r)^5730<BR>\n" );
document.write( "1+r is the annual growth factor.<BR>\n" );
document.write( "r is the annual growth rate.<BR>\n" );
document.write( "solve for (1+r) to get .5 ^ (1/5730) = 1+r = .9998790392.<BR>\n" );
document.write( "confirm this is true because .9998790392 ^ 5730 = .5<BR>\n" );
document.write( "if the scroll contains .76 * its original level of carbon-14, then you get:<BR>\n" );
document.write( ".76 = .9998790392 ^ x<BR>\n" );
document.write( "x is the number of years.<BR>\n" );
document.write( "take the log of both sides of the equation to get:<BR>\n" );
document.write( "log(.76) = x * log(.9998790392)<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = log(.76)/log(.9998790392) = 2268.671315.<BR>\n" );
document.write( "that's the number of years to get .76 * the carbon-14 in the artifact to become 76% of what it was when the artifact was new.<BR>\n" );
document.write( "that's how old the artifact is presumed to be based on the formula.<BR>\n" );
document.write( "this equation can be graphed as shown below.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/082201.jpg\"><BR>\n" );
document.write( "x represents the number of years from when the artifact was created.<BR>\n" );
document.write( "y represents the proportion of carbon-14 remaining.<BR>\n" );
document.write( "note that .5^(1/5730) is the annual growth factor which we had earlier determined to be .9998790392 rounded to the number of digits that could be displayed by my calculator. </SPAN>\n" );
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