1. 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?

2. Originally Posted by anf9292
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.