document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203016>Question 1203016</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1300 fish. Absent constraints, the population would grow by 200% per year. \r<BR>\n" );
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document.write( "If the starting population is given by P0 = 400, then after one breeding season the population of the pond is given by\r<BR>\n" );
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document.write( "P1 =    \r<BR>\n" );
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document.write( "After two breeding seasons the population of the pond is given by\r<BR>\n" );
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document.write( " P2= </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838266 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=838266\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "The logistic growth formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Pn=Po%2Br%281-Po%2Fk%29%2APo ALIGN=MIDDLE  ALT=\"+Pn=Po%2Br%281-Po%2Fk%29%2APo\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Where,  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r ALIGN=MIDDLE  ALT=\"+r\"   DISABLED_style= \"max-width:90%; height:auto;\" > - rate of population increase =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++2.0+ ALIGN=MIDDLE  ALT=\"++2.0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k ALIGN=MIDDLE  ALT=\"+k\"   DISABLED_style= \"max-width:90%; height:auto;\" >- carrying capacity of the pond = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1300+ ALIGN=MIDDLE  ALT=\"+1300+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Po ALIGN=MIDDLE  ALT=\"+Po\"   DISABLED_style= \"max-width:90%; height:auto;\" >- initial population =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++400 ALIGN=MIDDLE  ALT=\"++400\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Put the values in the formula,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Pn=400%2B2.0%281-400%2F1300%29%2A400 ALIGN=MIDDLE  ALT=\"+Pn=400%2B2.0%281-400%2F1300%29%2A400\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Pn=953 ALIGN=MIDDLE  ALT=\"+Pn=953\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In second generation,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Po+=+953 ALIGN=MIDDLE  ALT=\"+Po+=+953\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Pn=953%2B2.0%281-953%2F1300%29%2A953 ALIGN=MIDDLE  ALT=\"+Pn=953%2B2.0%281-953%2F1300%29%2A953\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Pn=1461 ALIGN=MIDDLE  ALT=\"+Pn=1461\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore, the population of fishes in the first generation will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=953 ALIGN=MIDDLE  ALT=\"953\"   DISABLED_style= \"max-width:90%; height:auto;\" > and in the second generation the population will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1461 ALIGN=MIDDLE  ALT=\"1461\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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