One hypothesis for a law of metabolism states that the metab

One hypothesis for a law of metabolism states that the metabolism of a creature is a function with B= a * m ^2/3, where B is the basal metabolic rate (in watts) of the animal and m is its mass (in kilograms).

(a) A human woman has an average mass of 60 kg and basal metabolic rate of 68 watts. Use this information to detemine the value of constant a in the power function.

(b) According to the model, what\'s the change of the basal metabolic rate for a woman whose weight loses from 60 kg to 55 kg.

(c) How large would an animal need to be in order to have a metabolic rate of 10,000 watss, according to the model?

Solution

B= a * m ^2/3, where B is the basal metabolic rate (in watts) of the animal and m is its mass (in kilograms).

a) m = 60 kgs; B = 58 watt

58 = a(60)^2/3

a = 58/60^2/3 = 58/15.347 = 3.779

b) Find B whne m= 55kg

B = 3.779*(55)^2/3 = 54.726 watts

Change in B from 60 to 55kg = 54.726 - 68 = -13.273 i.e. decrease in metabolic rate by 13.27 watts

c) B = 10,000

10,000 = 3.779*(m)^2/3

m = (10,000/3.779)^3/2 = 136123.98 kg size of animal