document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=821723>Question 821723</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bacteria culture started with 6500 bacteria and increased by 35% in the first 2 hours.\r<BR>\n" );
document.write( "\n" );
document.write( "How long does it take the population to triple in size? \r<BR>\n" );
document.write( "\n" );
document.write( "Use Q(t)=6500e^1.35/2(t) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #494366 by </B><A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><B>TimothyLamb(4379)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><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=TimothyLamb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=494366\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ---<BR>\n" );
document.write( "f(t)= P*e^(tk)<BR>\n" );
document.write( "where:<BR>\n" );
document.write( "P = initial value<BR>\n" );
document.write( "k = growth or decay factor per unit of time<BR>\n" );
document.write( "t = time<BR>\n" );
document.write( "---<BR>\n" );
document.write( "f(0) = P = 6500<BR>\n" );
document.write( "f(t)= 6500*e^(tk)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "f(2) = 6500*1.35 = 8775<BR>\n" );
document.write( "8775 = 6500*e^(2k)<BR>\n" );
document.write( "8775/6500 = e^(2k)<BR>\n" );
document.write( "ln(8775/6500) = ln( e^(2k) )<BR>\n" );
document.write( "ln(8775/6500) = 2k<BR>\n" );
document.write( "k = ln(8775/6500)/2<BR>\n" );
document.write( "k = 0.1500523 growth factor per hour<BR>\n" );
document.write( "---<BR>\n" );
document.write( "time to triple the population:<BR>\n" );
document.write( "f(t)= 3*6500 = 6500*e^(tk)<BR>\n" );
document.write( "3 = e^(tk)<BR>\n" );
document.write( "ln(3) = ln( e^(tk) )<BR>\n" );
document.write( "ln(3) = tk<BR>\n" );
document.write( "t = ln(3)/k<BR>\n" );
document.write( "t = 7.3215293<BR>\n" );
document.write( "---<BR>\n" );
document.write( "answer:<BR>\n" );
document.write( "time to triple the population = 7.3 hours = 7 hours and 19.3 minutes<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve and graph linear equations:<BR>\n" );
document.write( "https://sooeet.com/math/linear-equation-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve quadratic equations, quadratic formula:<BR>\n" );
document.write( "https://sooeet.com/math/quadratic-formula-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve systems of linear equations up to 6-equations 6-variables:<BR>\n" );
document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );