Question

According to a famous article by Max Kleiber*, the scaling of the metabolic rate or energy consumption for mammals Pₘₑₜₐᵦ (measured in kcal/day) with the body mass Mb (measured in kilograms) is Pₘₑₜₐᵦ = 70 Mb^(0.75).
What is the scaling exponent (the quantity x in a scaling law A = cMbx) for the specific metabolic rate as a function of the animal’s body mass?

Answer 1

From the question The scaling component ( x )  in the scaling law = 0.75

The metabolic rate of a mammal is the amount of energy a mammal uses up while at rest. This amount of energy accounts for the majority of energy used up by a mammal.

According to Max Kleber article the metabolic rate for mammals is measured as : Pₘₑₜₐᵦ = $70 Mb^{0.75}$  ------ ( 1 )

while  the scaling law ;

A = $cMb^x$  ------ ( 2 )

Equating ; equations ( 1 ) to ( 2 )  

The scaling exponent ( x ) in the scaling law is = 0.75

Hence the scaling component ( x ) in the scaling law = 0.75

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