document.write( "Question 1175054: 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.
\n" ); document.write( "If the population is given by po=600, then after one breeding season the population of the pond is given by
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\n" ); document.write( "After two breeding seasons the population of the pond is given by
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Algebra.Com's Answer #843387 by ikleyn(52788) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "Assume there is a certain population of fish in a pond whose growth is described
\n" ); document.write( "by the logistic equation. It is estimated that the carrying capacity for the pond is 1500 fish.
\n" ); document.write( "Absent constraints, the population would grow by 200% a year.
\n" ); document.write( "If the initial population is given by po= 600, then estimate the fish population in the pond
\n" ); document.write( "after one and two years
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\n" ); document.write( "\n" ); document.write( "One good Internet source for a beginner to read and to learn about a logistic equation is Libre text
\n" ); document.write( "https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/08%3A_Introduction_to_Differential_Equations/8.04%3A_The_Logistic_Equation\r
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\n" ); document.write( "\n" ); document.write( "This my post is to overlay calculations by the other tutor, that are irrelevant.\r
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document.write( "The general solution for the standard logistic differential equation is so called logistic function\r\n" );
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document.write( "    P(t) = .\r\n" );
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document.write( "Here  is the initial population, P(t) is current population, K is the carrying capacity \r\n" );
document.write( "and \"r\" is growth rate. Number \"e\" = 2.71828 is the base of natural logarithm \r\n" );
document.write( "(shown here as an approximate value).\r\n" );
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document.write( "In this current problem in the post, we are given\r\n" );
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document.write( "     = 600,  K = 1500,  r = 2.0.\r\n" );
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document.write( "They want you determine P(1) and P(2), the population after 1 and 2 years.\r\n" );
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document.write( "(a)  For t = 1 year\r\n" );
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document.write( "     P(1) =  = 1246.879478,  or 1247  (rounded).\r\n" );
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document.write( "(b)  For t = 2 years\r\n" );
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document.write( "     P(2) =  = 1459.89162,  or  1460  (rounded).\r\n" );
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\n" ); document.write( "\n" ); document.write( "Post-solution notice\r
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document.write( "    In my opinion, the question in the post is posed/worded INCORRECTLY.\r\n" );
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document.write( "    It asks about the breeding season, but we are not given information\r\n" );
document.write( "    for a breeding season - we are given information, related to years - so,\r\n" );
document.write( "    the question should be about the times of years, not the breeding seasons.\r\n" );
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document.write( "    The life of fish includes not only breeding - it includes also struggle for food, \r\n" );
document.write( "    survival from predators and diseases, natural death, that is, processes with a period of a year.\r\n" );
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