document.write( "Question 1206141: 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 1600 fish. Absent constraints, the population would grow by 120% per year.\r
\n" ); document.write( "\n" ); document.write( "If the starting population is given by ,p0=200 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 #843385 by ikleyn(52852) $\"\"$ $\"About$

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\n" ); document.write( "Assume there is a certain population of fish in a pond whose growth is described by the logistic equation.
\n" ); document.write( "It is estimated that the carrying capacity for the pond is 1600 fish. Absent constraints,
\n" ); document.write( "the population would grow by 120% per year.\r
\n" ); document.write( "\n" ); document.write( "If the starting population is given by p0=200, then estimate population of fish 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 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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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( "     = 200,  K = 1600,  r = 1.2.\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) =  = 514.74,  or 514  (rounded).\r\n" );
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document.write( "(b)  For t = 2 years\r\n" );
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document.write( "     P(2) =  = 978.58,  or  979  (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 breading 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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