document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1140192>Question 1140192</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Question Help <BR>\n" );
document.write( "The population of a colony of mosquitoes obeys the law of uninhibited growth.  If there are 1000 mosquitoes initially and there are 1400 after 1​ day, what is the size of the colony after <BR>\n" );
document.write( "3 ​days?  How long is it until there are 70,000 ​mosquitoes? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #760716 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=760716\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "There are good reasons in certain cases to use exponential growth using the natural base e.  But in this simple example it greatly complicates the solution.<br><BR>\n" );
document.write( "The population grew from 1000 to 1400 in 1 day; the daily growth factor is 1400/1000 = 1.4.  So the equation for the number of mosquitoes after n days is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28n%29+=+1000%281.4%29%5En ALIGN=MIDDLE  ALT=\"P%28n%29+=+1000%281.4%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(1) For the population after 3 days, evaluate the equation for n=3:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%283%29+=+1000%281.4%29%5E3+=+2744 ALIGN=MIDDLE  ALT=\"P%283%29+=+1000%281.4%29%5E3+=+2744\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The population is about 2744 after 3 days.<br><BR>\n" );
document.write( "(2) To find the number of days for the population to reach 70,000, set P=70000 and solve for n.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70000+=+1000%281.4%29%5En ALIGN=MIDDLE  ALT=\"70000+=+1000%281.4%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70+=+1.4%5En ALIGN=MIDDLE  ALT=\"70+=+1.4%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%2870%29%29+=+n%2Alog%28%281.4%29%29 ALIGN=MIDDLE  ALT=\"log%28%2870%29%29+=+n%2Alog%28%281.4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+log%28%2870%29%29%2Flog%28%281.4%29%29 ALIGN=MIDDLE  ALT=\"n+=+log%28%2870%29%29%2Flog%28%281.4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 12.626585 to several decimal places<br><BR>\n" );
document.write( "It takes about 12.6 days for the population to reach 70,000. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );