document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=242817>Question 242817</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How long will it take a sample of radioactive substance to decay to half of its original amount, if it decays according to the function A(t)=400e^0.045t, where t is the time in years?  Round to the nearest hunderedth year.<BR>\n" );
document.write( "The answeres could be <BR>\n" );
document.write( "A: 18.00 years<BR>\n" );
document.write( "B:  133.14 years<BR>\n" );
document.write( "C:  148.55 years<BR>\n" );
document.write( "D:  15.40 years<BR>\n" );
document.write( "I think the answer is 15.40 years.  Please let me know for sure. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #177827 by </B><A HREF=/tutors/aboutme.mpl?userid=MRperkins><B>MRperkins(300)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MRperkins><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=MRperkins><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=177827\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I am guessing that your original substance starts at 400 and you are looking to find when A(t)=200.<BR>\n" );
document.write( "In this case, you would have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2=e%5E.045t ALIGN=MIDDLE  ALT=\"1%2F2=e%5E.045t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To solve this, you would take the natural log (ln e) of both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%281%2F2%29=ln%28e%5E.045t%29 ALIGN=MIDDLE  ALT=\"ln%281%2F2%29=ln%28e%5E.045t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the rules of logarithms says that log (a/b)=log a - log b<BR>\n" );
document.write( "so, ln 1 -ln 2 =.045t<BR>\n" );
document.write( "use your calculator to finish this and you get t=-15.40 years.  I think your formula may have a negative missing or something.  I don't deal a lot with half life, but this is how you would do it and D is the right answer.\r<BR>\n" );
document.write( "\n" );
document.write( "For further questions, I can be reached at justin.sheppard.tech@hotmail.com </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );