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francois is stokcing a new fish pond on his farm. The pond is filling slowly and the volume of water in it can support a certain number of fish,(variable-F). F=42m+250, where m is the number of months the pond has been filling.

the pond was stocked initially with 110 fish, a population that will grow at a rate of 8 percent per month. P=110(1.08) to the power of m. this is the equation that models the population of fish after m number of months.

when will p equal f?
what will happen after this point has been reached? explain your answer.

  • Math -

    P = F when
    42 m + 250 = 110*1.08^m
    That equation can be solved by iteration. If m = 30,
    42 m + 250 = 1510
    110*1.08^m = 1106

    If m = 35
    F = 42 m + 250 = 1720
    P = 110*1.08^m = 1626

    If m = 36
    42 m + 250 = 1762
    110*1.08^m = 1756

    m is slightly more than 36 months

    At longer times, P will exceed F, and fish will start to die because the pond is too small to support the population.

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