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Math Help - allometric

  1. #1
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    allometric

    Consider an 8-year old child whose body mass is 25 kg and is increasing at a rate of 7 kg/year. Assuming that the mass of the kidneys scales with body mass as Mk=0.021 x Mb^0.85, find the rate at which the mass of the kidneys is increasing (in kg/year).

    For this problem..I basically used the weights 25kg,32kg,39kg, etc..increasing it by 7kg

    the Mk (mass of kidneys) keep increasing my .07. Would that be the answer?
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  2. #2
    MHF Contributor
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    Quote Originally Posted by anf9292 View Post
    Consider an 8-year old child whose body mass is 25 kg and is increasing at a rate of 7 kg/year. Assuming that the mass of the kidneys scales with body mass as Mk=0.021 x Mb^0.85, find the rate at which the mass of the kidneys is increasing (in kg/year).

    For this problem..I basically used the weights 25kg,32kg,39kg, etc..increasing it by 7kg

    the Mk (mass of kidneys) keep increasing my .07. Would that be the answer?
    Mk = (0.021)(Mb)^0.85
    Differentiate both sides,
    d(Mk) = 0.021[(0.85)(Mb)^(-0.15)]*d(Mb)
    d(Mk) = (0.01785)d(Mb) / (Mb)^0.15 ----------(i)

    Given:
    Mb = 25 k
    d(Mb) = 7 kg/yr
    So,
    d(Mk) = (0.01785)(7) / (25)^0.15 = 0.077 kg/yr.

    If the Mb = 25 +7 = 32 kg,
    d(Mk) = (0.01785)(7) / (32)^0.15 = 0.0743 kg/yr

    If the Mb = 32 +7 = 39 kg,
    d(Mk) = (0.01785)(7) / (39)^0.15 = 0.0721 kg/yr

    Therfore, no, the rate of change of the kidney mass is decreasing as the boy's body mass is increasing. -------------answer.
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