Question

A study finds that the metabolic rate of mammals is proportional to m3/4, where m is the total body mass. By what factor does the metabolic rate of a 70.0-kg humanexceed that of a 4.77-kg cat?Numeric Response

Answer 1

7.5

Explanation:

The mass factor of a human which exceeds that of a cat would be found by using the following expression:

`\begin{gathered} m^{(3)/(4)} \\ m\text{ is the mass of total body} \end{gathered}`

Mass of human will be calculated in metabolic process by using the following equation:

`\begin{gathered} R_H\propto(m^{}_H)^{(3)/(4)} \\ R_H\text{ is the metabolic rate of human and }m_H\text{ is the mass of the human} \end{gathered}`

Mass of cat will be calculated in metabolic process by using the following equation:

`\begin{gathered} R_C\propto(m^{}_C)^{(3)/(4)} \\ R_C\text{ is the metabolic rate of cat and }m_C\text{ is the mass of the cat} \end{gathered}`

The mass factor of a human that exceeds that of a cat would be found as below.

`\begin{gathered} (R_H)/(R_C)=\frac{(m^{}_H)^{(3)/(4)}}{(m^{}_C)^{(3)/(4)}}_{} \\ (R_H)/(R_C)=(\frac{m_H}{m^{}_C})^{(3)/(4)} \end{gathered}`

Replacing:

`\begin{gathered} (R_H)/(R_C)=(\frac{70}{4.77^{}_{}})^{(3)/(4)} \\ (R_H)/(R_C)=7.497\cong7.5 \end{gathered}`

Therefore, the metabolic rate of a 70 kg human by a factor 7.5 that of a 4.77 kg cat