# allometric

• Jan 20th 2007, 06:49 PM
anf9292
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?
• Jan 21st 2007, 11:58 AM
ticbol
Quote:

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.