document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1157061>Question 1157061</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A piece of charcoal is found to contain 39​% of the element B that it originally had.<BR>\n" );
document.write( "​(a) When did the tree from which the charcoal came​ die? Use 5800 years as the​ half-life of  the element B.<BR>\n" );
document.write( "​(b) Using a graphing​ utility, graph the relation between the percentage of the element B remaining and time.<BR>\n" );
document.write( "​(c) Using​ INTERSECT, determine the time that elapses until half of the the element B remains.<BR>\n" );
document.write( "​(d) Verify the answer found in part ​(a). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #779927 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=779927\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A piece of charcoal is found to contain 39​% of the element B that it originally had.<BR>\n" );
document.write( "Use 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 = time of decay<BR>\n" );
document.write( "h = half life of substance<BR>\n" );
document.write( ":<BR>\n" );
document.write( "​(a) When did the tree from which the charcoal came​ die?<BR>\n" );
document.write( " Use 5800 years as the​ half-life of the element B.<BR>\n" );
document.write( "Assuming initial amt is 1<BR>\n" );
document.write( "2^(-t/5800) = .39<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t%2F5800 ALIGN=MIDDLE  ALT=\"-t%2F5800\"   DISABLED_style= \"max-width:90%; height:auto;\" >ln(2) = ln(.39)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t%2F5800 ALIGN=MIDDLE  ALT=\"-t%2F5800\"   DISABLED_style= \"max-width:90%; height:auto;\" >= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28.39%29%2Fln%282%29 ALIGN=MIDDLE  ALT=\"ln%28.39%29%2Fln%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t%2F5800 ALIGN=MIDDLE  ALT=\"-t%2F5800\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -1.35845<BR>\n" );
document.write( "t = -5800 * -1.3845<BR>\n" );
document.write( "t = 7879 yrs<BR>\n" );
document.write( ": <BR>\n" );
document.write( "​(b) Using a graphing​ utility, graph the relation between the percentage of the <BR>\n" );
document.write( " element B remaining and time.<BR>\n" );
document.write( "the equation for this: y = 100*2^(-x/5800)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-2000%2C+15000%2C+-20%2C+105%2C+100%2A2%5E%28-x%2F5800%29%2C+50%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-2000%2C+15000%2C+-20%2C+105%2C+100%2A2%5E%28-x%2F5800%29%2C+50%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "​(c) Using​ INTERSECT, determine the time that elapses until half of the the <BR>\n" );
document.write( " element B remains. Did that<BR>\n" );
document.write( ":<BR>\n" );
document.write( "​(d) Verify the answer found in part ​(a). confirmed, entered 7879 and got 39 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );