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Math Help - integral calculas???

  1. #1
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    Post integral calculas???

    r(t)=dr/dt=0.05e^.02t (200-t)

    r(0)=1000

    using integral calculas i need to show that r(t)=2.5e^.02t (250-t)+375

    How is this found???
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    Your question is a little unreadable.

    But I could see that you need to solve a differential equation with initial condition.
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  3. #3
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    Exclamation is this a little easier to understand???

    If the rate of growth of the number of wasps at time t days is given by -

    r(t)=dr/dt=0.05e^.02t (200-t), r(0)=1000

    show that the number of reproductive wasp r(t) at time t equals -

    2.5e^.02t (250-t)+375

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  4. #4
    MHF Contributor kalagota's Avatar
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    Taguig City, Philippines
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    Quote Originally Posted by softdrink_jr View Post
    If the rate of growth of the number of wasps at time t days is given by -

    r(t)=dr/dt=0.05e^.02t (200-t), r(0)=1000

    show that the number of reproductive wasp r(t) at time t equals -

    2.5e^.02t (250-t)+375
    is this what you want?

    r(t) = \frac{dr}{dt} = 0.05e^{0.02t}(200 - t)
    where \, r(0)=1000

    and show that
    r(t) = 2.5e^{.02t} (250-t)+375

    but why is that \, r(t) = \frac{dr}{dt}?
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