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)^0.85Originally Posted by anf9292
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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