document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1175054>Question 1175054</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 1500 fish. Absent constraints, the population would grow by 200% a year. <BR>\n" );
document.write( "If the population is given by po=600, then after one breeding season the population of the pond is given by<BR>\n" );
document.write( "p1=<BR>\n" );
document.write( "After two breeding seasons the population of the pond is given by<BR>\n" );
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 #800576 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=800576\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if the growth is 200% per year, then the growth rate is 2 per year.<BR>\n" );
document.write( "the formula for future value is f = p * (1 + r) ^ n<BR>\n" );
document.write( "f is the future value<BR>\n" );
document.write( "p is the present value<BR>\n" );
document.write( "r is the rat4e of growth per year.<BR>\n" );
document.write( "n is the number of years.\r<BR>\n" );
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document.write( "in your problem, the formula becomes f = 600 * (1 + 2) ^ n\r<BR>\n" );
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document.write( "p1 is the number at the end of 1 year.<BR>\n" );
document.write( "p2 is the number at the end of 2 years.\r<BR>\n" );
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document.write( "p1 = 600 * 3^1 = 1800<BR>\n" );
document.write( "p2 = 600 * 3^2 = 5400\r<BR>\n" );
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document.write( "how does this work?\r<BR>\n" );
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document.write( "the population is 600 in p0.<BR>\n" );
document.write( "the growth is 200% per year, meaning the growth is 1200 from p0 to p1.<BR>\n" );
document.write( "the population is 600 + 1200 = 1800 in p1.<BR>\n" );
document.write( "the growth is 200% per year, meaning the growth is 3600 from p1 to p2.<BR>\n" );
document.write( "the population is 1800 + 3600 = 5400 in p2.\r<BR>\n" );
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document.write( "since the carrying capacity of the pond is 1500 fish, it's pretty clear that there's not a lot of room for growth.<BR>\n" );
document.write( "at the given growth rate of 200% per year, the pond is over capacity at the end of 1 year.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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