document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206832>Question 1206832</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The population of a colony of rabbits grows exponentially. The colony begins with 5 rabbits; 5 years later there are 320 rabbits.<BR>\n" );
document.write( "(a) estimate how long it takes for the population of rabbits to reach 1000 rabbits. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844505 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=844505\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let population og rabbits be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   DISABLED_style= \"max-width:90%; height:auto;\" >, time <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in years)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28t%29=a%2Ae%5E%28b%2At%29 ALIGN=MIDDLE  ALT=\"p%28t%29=a%2Ae%5E%28b%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if the colony begins with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+ ALIGN=MIDDLE  ALT=\"5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >rabbits, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%280%29=5 ALIGN=MIDDLE  ALT=\"p%280%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5=a%2Ae%5E%28b%2A0%29 ALIGN=MIDDLE  ALT=\"5=a%2Ae%5E%28b%2A0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5=a%2A1 ALIGN=MIDDLE  ALT=\"5=a%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=5 ALIGN=MIDDLE  ALT=\"a=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "so far equation is\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28t%29=5%2Ae%5E%28b%2At%29 ALIGN=MIDDLE  ALT=\"p%28t%29=5%2Ae%5E%28b%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > years later there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=320 ALIGN=MIDDLE  ALT=\"320\"   DISABLED_style= \"max-width:90%; height:auto;\" > rabbits\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=320=5%2Ae%5E%28b%2A5%29 ALIGN=MIDDLE  ALT=\"320=5%2Ae%5E%28b%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=320%2F5=e%5E%28b%2A5%29 ALIGN=MIDDLE  ALT=\"320%2F5=e%5E%28b%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28b%2A5%29=64 ALIGN=MIDDLE  ALT=\"e%5E%28b%2A5%29=64\"   DISABLED_style= \"max-width:90%; height:auto;\" >...take natural log of both sides\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28e%5E%28b%2A5%29%29=ln%2864%29 ALIGN=MIDDLE  ALT=\"ln%28e%5E%28b%2A5%29%29=ln%2864%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%2A5%29ln%28e%29=ln%2864%29 ALIGN=MIDDLE  ALT=\"%28b%2A5%29ln%28e%29=ln%2864%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%2A5%29%2A1=4.1588830833596715 ALIGN=MIDDLE  ALT=\"%28b%2A5%29%2A1=4.1588830833596715\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=4.1588830833596715%2F5 ALIGN=MIDDLE  ALT=\"b=4.1588830833596715%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=0.8317766166719343 ALIGN=MIDDLE  ALT=\"b=0.8317766166719343\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "equation is:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28t%29=5%2Ae%5E%280.8317766166719343%2At%29 ALIGN=MIDDLE  ALT=\"p%28t%29=5%2Ae%5E%280.8317766166719343%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(a) estimate how long it takes for the population of rabbits to reach <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000 ALIGN=MIDDLE  ALT=\"1000\"   DISABLED_style= \"max-width:90%; height:auto;\" > rabbits.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000=5%2Ae%5E%280.8317766166719343%2At%29 ALIGN=MIDDLE  ALT=\"1000=5%2Ae%5E%280.8317766166719343%2At%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%280.8317766166719343%2At%29=200 ALIGN=MIDDLE  ALT=\"e%5E%280.8317766166719343%2At%29=200\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28e%5E%280.8317766166719343%2At%29%29=ln%28200%29 ALIGN=MIDDLE  ALT=\"ln%28e%5E%280.8317766166719343%2At%29%29=ln%28200%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.8317766166719343%2At%29%2Aln%28e%29=ln%28200%29 ALIGN=MIDDLE  ALT=\"%280.8317766166719343%2At%29%2Aln%28e%29=ln%28200%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.8317766166719343%2At=5.298317366548 ALIGN=MIDDLE  ALT=\"0.8317766166719343%2At=5.298317366548\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=5.298317366548%2F0.8317766166719343 ALIGN=MIDDLE  ALT=\"t=5.298317366548%2F0.8317766166719343\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=6.37+ ALIGN=MIDDLE  ALT=\"t=6.37+\"   DISABLED_style= \"max-width:90%; height:auto;\" >years\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );