document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=979620>Question 979620</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An experiment is carried out in which the number n of bacteria in a liquid, is given by the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=650e%5E%28kt%29 ALIGN=MIDDLE  ALT=\"n=650e%5E%28kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where t is the time in minutes after the beginning of the experiment and k is a constant. The number of bacteria doubles every 20 minutes. Find the exact value of k. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #600912 by </B><A HREF=/tutors/aboutme.mpl?userid=Cromlix><B>Cromlix(4381)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Cromlix><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=Cromlix><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=600912\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi there,<BR>\n" );
document.write( "n = 650e^kt<BR>\n" );
document.write( "The current value for the bacteria = 650<BR>\n" );
document.write( "If the number doubles then n = 1300<BR>\n" );
document.write( "So n = 650e^kt<BR>\n" );
document.write( "=> 1300 = 650e^20k<BR>\n" );
document.write( "=> 1300/650 = e^20k<BR>\n" );
document.write( "=> 2 = e^20k<BR>\n" );
document.write( "=> log(base e)2 = 20k log(base e) e <BR>\n" );
document.write( "log(base e)e = 1<BR>\n" );
document.write( "=> log(base e)2 = 20k<BR>\n" );
document.write( "=> k = log(base e)2/20<BR>\n" );
document.write( "=> k = 0.03466 (to 5 decimal places)<BR>\n" );
document.write( "Hope this helps:-)  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );