document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=271545>Question 271545</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the population of a colony of bateria is growing exponentially according to the function below , where t is the time in hours. how long will it take for the  population of the colony to grow to 1,000 B(t)=12*e^0.2t </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #198778 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=198778\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the population of a colony of bacteria is growing exponentially according to the function below , where t is the time in hours. how long will it take for the population of the colony to grow to 1,000 B(t)=12*e^0.2t<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2Ae%5E%280.2t%29 ALIGN=MIDDLE  ALT=\"12%2Ae%5E%280.2t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1000<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%280.2t%29 ALIGN=MIDDLE  ALT=\"e%5E%280.2t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000%2F12 ALIGN=MIDDLE  ALT=\"1000%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the nat logs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28e%5E%280.2t%29%29 ALIGN=MIDDLE  ALT=\"ln%28e%5E%280.2t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%281000%2F12%29 ALIGN=MIDDLE  ALT=\"ln%281000%2F12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.2t%2Aln%28e%29 ALIGN=MIDDLE  ALT=\".2t%2Aln%28e%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%281000%2F12%29 ALIGN=MIDDLE  ALT=\"ln%281000%2F12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "nat log of e is 1, so we have<BR>\n" );
document.write( ".2t = 4.22848<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.22848%2F.2 ALIGN=MIDDLE  ALT=\"4.22848%2F.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = 22.1142 hrs to reach 1000<BR>\n" );
document.write( ";<BR>\n" );
document.write( "Check on a calc using t=22.1142<BR>\n" );
document.write( "enter: 12*e^(.2*22.1142) = 999.99 ~1000 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );