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Math Help - Circular Functions Application #2

  1. #1
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    Circular Functions Application #2

    scientists studying a population of a particular species of moth determine that the size of the population, N (in thousands), at time t weeks after the commencement of the study, can be modelled by the equation N= 2sin(pi(t)/5)+3, 0≤t≤40.

    A) state the initial size of the population?
    B) find the size of the population when it is a: i) minimum ii) maximum
    C)what is the size of the population after 8 weeks? Give your answear correct to the nearest hundred.
    D) on which day of the study does the population first exceed 4000 moths?

    please help i understand them.
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  2. #2
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    A) t=0 N = 3
    B) sinus is minimum with the value -1, and maximum 1, so N is minimum at N=2*(-1)+3=1, and maximum N = 2*1+3 = 5
    C) t=8 N = 2sin(pi*8/5)+3 = (calculator DRG to rad) = 1.097886...=1.100 thousends. Size is 1100
    D) N = 4, 4-3=2sin(pi(t)/5) , 0.5 = sin(pi(t)/5) , use 0.5 sin-1, pi*t/5 = 0.523598..., t = 0.8333 weeks, 0.8333*7=5.8333. On the fifth day the population exceed 4000.
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