document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=155617>Question 155617</A>: <I><SPAN STYLE=\"word-break: break-all;\"> After 5 hours an initial bacteria population of 100 members has increased in size to 500 members. Determine the exponential growth rate of the colony of bacteria. \r<BR>\n" );
document.write( "\n" );
document.write( "I'm very confused by this word problem. I'd like the correct answer and to be able to learn how to come to that answer. Thank you for all your help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #114669 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=114669\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> OK, first, you know that you have exponential growth, <BR>\n" );
document.write( "your equation looks like this,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%28t%29=N%5B0%5De%5E%28%28alpha%2At%29%29 ALIGN=MIDDLE  ALT=\"N%28t%29=N%5B0%5De%5E%28%28alpha%2At%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use your conditions to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%5B0%5D ALIGN=MIDDLE  ALT=\"N%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha ALIGN=MIDDLE  ALT=\"alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Initially, at t=0 hours, N=100<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%280%29=N%5B0%5De%5E%28%28alpha%2A0%29%29=100 ALIGN=MIDDLE  ALT=\"N%280%29=N%5B0%5De%5E%28%28alpha%2A0%29%29=100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%5B0%5D=100 ALIGN=MIDDLE  ALT=\"N%5B0%5D=100\"   DISABLED_style= \"max-width:90%; height:auto;\" > since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E0=1 ALIGN=MIDDLE  ALT=\"e%5E0=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "At 5 hours, N=500,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%285%29=100e%5E%28%28alpha%2A5%29%29=500 ALIGN=MIDDLE  ALT=\"N%285%29=100e%5E%28%28alpha%2A5%29%29=500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28%28alpha%2A5%29%29=5 ALIGN=MIDDLE  ALT=\"e%5E%28%28alpha%2A5%29%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha%2A5=ln%285%29 ALIGN=MIDDLE  ALT=\"alpha%2A5=ln%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha=ln%285%29%2F5 ALIGN=MIDDLE  ALT=\"alpha=ln%285%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha=0.322 ALIGN=MIDDLE  ALT=\"alpha=0.322\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Put it all together,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%28t%29=100e%5E%28%280.322%2At%29%29 ALIGN=MIDDLE  ALT=\"N%28t%29=100e%5E%28%280.322%2At%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );