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Math Help - trig formula for a population

  1. #1
    Senior Member furor celtica's Avatar
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    trig formula for a population

    The population, P, of a certain type of bird on a remote island varies during the course of a year according to feeding, breeding, migratory seasons and predator interactions. An ornithologist doing research into bird numbers for this species attempts to model the population on the island with the annually periodic equation
    P = N Ccoswt
    Where N, C and w are constants, and t is the time in weeks, with t = 0 representing midnight on the first of January.
    a. Taking the period of this function to be 50 weeks, find the value of w.
    b. Use the equation to describe, in terms of N and C,
    (i) the number of birds of this species on the island at the start of each year;
    (ii) the maximum number of these birds, and the time of year when this occurs

    My answers were
    a. w=7.2
    b. (i) P=N-C
    These were correct

    For b. (ii) I gave
    P=N+C, t=25 weeks

    However the answer is P=N+C for t=37.5 weeks.

    How is this possible?
    P=N+C when coswt=-1, therefore when t= (arcos(-1))/w = 180/7.2 = 25

    ?
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  2. #2
    MHF Contributor
    skeeter's Avatar
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    Re: trig formula for a population

    with the function given, max occurs at t = T/2 ... the "answer" is incorrect.

    an aside ... what is the source of these problems? reason I ask is that most times problems that model trig functions use radians rather than degrees.
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  3. #3
    Senior Member furor celtica's Avatar
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    Re: trig formula for a population

    A level mathematics for Cambridge International Examinations, Pure Mathematics 1
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