document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183428>Question 1183428</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 2000 fish. Absent constraints, the population would grow by 210% per year.\r<BR>\n" );
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document.write( "If the starting population is given by p0=500, then after one breeding season the population of the pond is given by\r<BR>\n" );
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document.write( "p1 =<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" );
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document.write( "Logistic equation is y=L/(1+be^(-kt)) and dP/dT=kP(1- (P/L))<BR>\n" );
document.write( "L=2000, the carrying capacity.<BR>\n" );
document.write( "k=constant of proportionality, or 2.1<BR>\n" );
document.write( "Using the first,<BR>\n" );
document.write( "t=0; 500=2000/(1+be^0)<BR>\n" );
document.write( "500(1+b)=2000<BR>\n" );
document.write( "b=3<BR>\n" );
document.write( "t=1 season<BR>\n" );
document.write( "y(1)=2000/(1+3e^(-2.1)=1462.66 or 1463<BR>\n" );
document.write( "y(2)=2000/(1+3e^(-4.2))=1913.90 or 1914\r<BR>\n" );
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