A population of insects increases at a rate of 250 + 16t +0.3t^2 insects per day. Find the insect population after 3 days, assuming that there are 40 insects at t=0.

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  1. d(Insects)/dt = 250 + 16t + .3t^2

    so Insects = 250t + 8t^2 + .1t^3 + c
    when t=0, Insects = 40, so c = 40

    Insects = 250t + 8t^2 + .1t^3 + 40

    when t = 3
    Insects = 750 + 72 + 2.7 + 40
    = appr 865

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