document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193432>Question 1193432</A>: <I><SPAN STYLE=\"word-break: break-all;\"> MAT 145: Topics In Contemporary Math\r<BR>\n" );
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document.write( "     20: Logistic Growth\r<BR>\n" );
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document.write( "1) The population of fuzzy quadrupeds increases by 50%) every month after they are <BR>\n" );
document.write( "introduced to a new region. Suppose 30 fuzzy quadrupeds are accidentally introduced to <BR>\n" );
document.write( "Springfield when a family visited the region to which fuzzy quadrupeds are native. <BR>\n" );
document.write( "However, Springfield only has a carrying capacity of 70 fuzzy quadrupeds. How many <BR>\n" );
document.write( "fuzzy quadrupeds would there be for each of the first five months after they were <BR>\n" );
document.write( "introduced to the new region?<BR>\n" );
document.write( "Month Formula Population size<BR>\n" );
document.write( "0 Beginning population<BR>\n" );
document.write( "1<BR>\n" );
document.write( "2<BR>\n" );
document.write( "3<BR>\n" );
document.write( "4<BR>\n" );
document.write( "5<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825613 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=825613\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
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document.write( "(Answered the other day for (perhaps) a different student...)<br><BR>\n" );
document.write( "Solution copied here.<br><BR>\n" );
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document.write( "Here is a logistic growth formula:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=L%2F%281%2Ba%2Ae%5E%28-bt%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=L%2F%281%2Ba%2Ae%5E%28-bt%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "L is the carrying capacity, given as 70.<br><BR>\n" );
document.write( "a and b are constants to be determined from the given information.<br><BR>\n" );
document.write( "The initial population, f(0), is 30:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=70%2F%281%2Ba%2Ae%5E0%29=70%2F%281%2Ba%29=30 ALIGN=MIDDLE  ALT=\"f%280%29=70%2F%281%2Ba%2Ae%5E0%29=70%2F%281%2Ba%29=30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70=30%281%2Ba%29=30%2B30a ALIGN=MIDDLE  ALT=\"70=30%281%2Ba%29=30%2B30a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40=30a ALIGN=MIDDLE  ALT=\"40=30a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=40%2F30=4%2F3 ALIGN=MIDDLE  ALT=\"a=40%2F30=4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The population increases by 50% each month, so the population after one month is 1.5(30)=45:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45=70%2F%281%2B%284%2F3%29e%5E%28%28-b%281%29%29%29%29 ALIGN=MIDDLE  ALT=\"45=70%2F%281%2B%284%2F3%29e%5E%28%28-b%281%29%29%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=70=45%281%2B%284%2F3%29e%5E%28-b%29%29 ALIGN=MIDDLE  ALT=\"70=45%281%2B%284%2F3%29e%5E%28-b%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=70=45%2B60e%5E%28-b%29 ALIGN=MIDDLE  ALT=\"70=45%2B60e%5E%28-b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25=60e%5E%28-b%29 ALIGN=MIDDLE  ALT=\"25=60e%5E%28-b%29\"   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-b%29=25%2F60=5%2F12 ALIGN=MIDDLE  ALT=\"e%5E%28-b%29=25%2F60=5%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b=ln%285%2F12%29 ALIGN=MIDDLE  ALT=\"-b=ln%285%2F12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > =-0.87547 to 5 decimal places<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=0.87547 ALIGN=MIDDLE  ALT=\"b=0.87547\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28n%29=70%2F%281%2B%284%2F3%29e%5E%28%28-0.87547%29n%29%29 ALIGN=MIDDLE  ALT=\"f%28n%29=70%2F%281%2B%284%2F3%29e%5E%28%28-0.87547%29n%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That function gives the following populations after n months to fill your chart:<br><PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "  months   population  (rounded)\r\n" );
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document.write( "    0      30             30\r\n" );
document.write( "    1      45             45\r\n" );
document.write( "    2      56.842         57\r\n" );
document.write( "    3      63.842         64\r\n" );
document.write( "    4      67.296         67\r\n" );
document.write( "    5      68.847         69\r\n" );
document.write( "    .\r\n" );
document.write( "    .\r\n" );
document.write( "    .\r\n" );
document.write( "   10      69.985         70</PRE> </SPAN>\n" );
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