Question

According to a famous article by Max Kleiber, the scaling of the metabolic rate or energy consumption for mammals Pmetab (measured in kcal/day) with the body mass Mb (measured in kilograms) is Pmetab=70M0.75b.
a. What is the specific metabolic rate, i.e. the metabolic rate per kilogram of body mass for the following animals?a mouse whose mass is 30g. Give your answer to three significant figures.
b. What is the specific metabolic rate, i.e. the metabolic rate per kilogram of body mass for the following animals?a cow whose mass is 300kg. Give your answer to three significant figures.

Answer 1

Answer:

Explanation:

Given that:

The scaling of the specific metabolic rate is:

$=\dfrac{P_{metab}}{m}$

where;

$P_{metab} = 70M_b^{0.75}$

$=\dfrac{ 70M_b^{0.75}}{m}$

(a) For a mouse whose mass = 30 g = 0.030 kg

The specific metabolic rate $=\dfrac{ 70*(0.030)^{0.75}}{(0.030)}$

= 168.197 kg

≅ 168 kg to 3 significant fig.

(a) For a cow whose mass = 300 kg

The specific metabolic rate $=\dfrac{ 70*(300)^{0.75}}{(300)}$

= 16.8197 kg

≅ 16.8 kg to 3 significant fig.