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Math Help - differential equation

  1. #1
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    differential equation

    If we assume that a person's weight depends on the energy consumed minus energy ued, one model is that weight changes in proportion to the difference, so:

    dw/dt = k(C - 38.5w) where w(0) = w subscript 0

    where w(t) kg is the weight at t days, C is the daily calorie intake, and we assume 38.5 calories per kg per day are used

    (i) if you wish to maintain a constant weight of 82 kg, what should be your daily calorie intake C?

    (ii) If you weigh 100 kg, and you want to lose 10 kg in a month, what should C be? (Assume k = 1.3 * 10^(-4) kg/calorie and a month of 30 days) Is this result healthy?

    can someone solve these questions for me, they are on a past test paper which does not have solutions available.
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  2. #2
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    Quote Originally Posted by razorfever View Post
    If we assume that a person's weight depends on the energy consumed minus energy ued, one model is that weight changes in proportion to the difference, so:

    dw/dt = k(C - 38.5w) where w(0) = w subscript 0

    where w(t) kg is the weight at t days, C is the daily calorie intake, and we assume 38.5 calories per kg per day are used

    (i) if you wish to maintain a constant weight of 82 kg, what should be your daily calorie intake C?

    (ii) If you weigh 100 kg, and you want to lose 10 kg in a month, what should C be? (Assume k = 1.3 * 10^(-4) kg/calorie and a month of 30 days) Is this result healthy?

    can someone solve these questions for me, they are on a past test paper which does not have solutions available.
    (i) \frac{dw}{dt} = 0 ... solve for C

    (ii) solve \int \frac{dw}{C - 38.5w} = \int k \, dt with initial condition w(0) = 100.

    after you find w(t), set w(30) = 90 and solve for C.
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  3. #3
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    can u help me out the same way with that kind of template for some of my other posts about differential equation word problems?
    I have an exam coming up and my prof hasn't touched any word problems,
    if you could provide templates, i can understand them better and hopefully pass the exam

    links:
    http://www.mathhelpforum.com/math-he...tric-func.html

    http://www.mathhelpforum.com/math-he...d-problem.html

    http://www.mathhelpforum.com/math-he...-diver-de.html

    http://www.mathhelpforum.com/math-he...ates-flow.html

    http://www.mathhelpforum.com/math-he...72473-ivp.html

    http://www.mathhelpforum.com/math-he...ntial-eqn.html

    thanks in advance
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  4. #4
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    can you tell me what your final answer for C is?
    i'm getting 102375.57

    as for the constant in part (i) i'm getting (C - 3850)
    and the expression for C in part (ii) i'm getting
    [3465 - 3850e^(30k)] / [1 - e^(30k)]

    is this correct
    can someone show me the correct solution step by step?
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  5. #5
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    \int \frac{dw}{C - 38.5w} = \int k \, dt

    \int \frac{-38.5}{C - 38.5w} \, dw = -38.5\int k \, dt

    \ln|C - 38.5w| = -38.5kt + A

    C - 38.5w = Be^{-38.5kt}

    w(0) = 100

    C - 3850 = B

    C - 38.5w = (C - 3850)e^{-38.5kt}

    C - 38.5w = Ce^{-38.5kt} - 3850e^{-38.5kt}

    C - Ce^{-38.5kt} = 38.5w - 3850e^{-38.5kt}

    C(1 - e^{-38.5kt}) = 38.5w - 3850e^{-38.5kt}

    C = \frac{38.5w - 3850e^{-38.5kt}}{1 - e^{-38.5kt}}

    w(30) = 90 ... C \approx 1090 \, cal
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  6. #6
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    now i'm getting C = 3515
    how do you do that last part w(30) = 90
    do u rearrange and make w the subject then put t=30 and solve for C right?
    can u show me that last step explicitly??
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  7. #7
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    Quote Originally Posted by razorfever View Post
    now i'm getting C = 3515
    how do you do that last part w(30) = 90
    do u rearrange and make w the subject then put t=30 and solve for C right?
    can u show me that last step explicitly??


    since the task was to find C, I solved for C ... sub in 90 for w, 30 for t, and the given value for k (0.00013 , correct?)
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  8. #8
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    yeah i just realized i was making a careless mistake
    i wasn't putting E in my calculator , instead just getting the value of
    (-38.5 * 0.00013 * 30) and this was giving me C as 3515 but I got it now
    thanks for all your help!
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  9. #9
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    Quote Originally Posted by razorfever View Post
    can u help me out the same way with that kind of template for some of my other posts about differential equation word problems?
    I have an exam coming up and my prof hasn't touched any word problems,
    if you could provide templates, i can understand them better and hopefully pass the exam

    links:
    http://www.mathhelpforum.com/math-he...tric-func.html

    http://www.mathhelpforum.com/math-he...d-problem.html

    http://www.mathhelpforum.com/math-he...-diver-de.html

    http://www.mathhelpforum.com/math-he...ates-flow.html

    http://www.mathhelpforum.com/math-he...72473-ivp.html

    http://www.mathhelpforum.com/math-he...ntial-eqn.html

    thanks in advance
    none of your links are working
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