Chapter 6.4, Problem 57PPS

To determine

The metabolism $\left(P\right)$ for the animals of given mass $\left(m\right)$ in kilogram written below using the Kleiber’s Law $P=73.3\sqrt[4]{m^3}$ .

Animal	Mass(kg)
Bald eagle	4.5
Golden retriever	30
Komodo dragon	72
Bottlenose dolphin	156
Asian elephant	2300

Answer to Problem 57PPS

The metabolism for bald eagle is 226.47, for golden retriever 939.60, for komodo dragon 1811.77, for bottlenose dolphin 3235.54 and for Asian elephant 24344.4.

Explanation of Solution

Given information: The mass of the animals is shown in table below.

Animal	Mass(kg)
Bald eagle	4.5
Golden retriever	30
Komodo dragon	72
Bottlenose dolphin	156
Asian elephant	2300

Also the metabolism $\left(P\right)$ of the animals for the given mass can be evaluated using the formula,

  $P=73.3\sqrt[4]{m^3}\mathrm{......}\left(1\right)$

Calculation: From (1) the metabolism of the animals can be evaluated.

For bald eagle mass $\left(m=4.5kg\right)$ , therefore metabolism $P_{baldeagle}$ is evaluated as,

  $\begin{array}{c}{P}_{baldeagle}=73.3\sqrt[4]{{\left(4.5\right)}^3}\mathrm{......}\left(\text{For }m=4.5\right)\\ =226.47\end{array}$

For golden retriever mass $\left(m=30kg\right)$ , therefore metabolism $P_{goldenretriever}$ is evaluated as,

  $\begin{array}{c}{P}_{goldenretriever}=73.3\sqrt[4]{{\left(30\right)}^3}\mathrm{......}\left(\text{For }m=30\right)\\ =939.60\end{array}$

For Komodo dragon mass $\left(m=72kg\right)$ , therefore metabolism $\left(P_{ko\mathrm{mod}odragon}\right)$ is evaluated as,

  $\begin{array}{c}{P}_{ko\mathrm{mod}odragon}=73.3\sqrt[4]{{\left(72\right)}^3}\mathrm{......}\left(\text{For }m=72\right)\\ =1811.77\end{array}$

For bottlenose dolphin mass $\left(m=72kg\right)$ , therefore metabolism $\left(P_{bottlenosedolphin}\right)$ is evaluated as,

  $\begin{array}{c}{P}_{bottlenosedolphin}=73.3\sqrt[4]{{\left(156\right)}^3}\mathrm{......}\left(\text{For }m=156\right)\\ =3235.54\end{array}$

For Asian elephant mass $\left(m=2300kg\right)$ , therefore metabolism $\left(P_{asianelephant}\right)$ is evaluated as,

  $\begin{array}{c}{P}_{asianelephant}=73.3\sqrt[4]{{\left(2300\right)}^3}\mathrm{......}\left(\text{For }m=2300\right)\\ =24344.4\end{array}$