Chapter 6 Powers and Roots

We next turn our attention to a large and useful family of functions, called power functions. Here is an example of a power function with fractional exponents.
In 1932, Max Kleiber published a remarkable equation for the metabolic rate of an animal as a function of its mass. The table at right shows the mass of various animals in kilograms and their metabolic rates, in kilocalories per day. A plot of the data, resulting in the famous “mouse-to-elephant” curve, is shown in the figure.
Animal | Mass (kg) | Metabolic rate (kcal/day) |
Mouse | ||
Rat | ||
Guinea pig | ||
Cat | ||
Rabbit | ||
Dog | ||
Chimpanzee | ||
Sheep | ||
Human | ||
Pig | ||
Cow | ||
Polar bear | ||
Elephant |
Kleiber modeled his data by the power function
where is the metabolic rate and is the mass of the animal. Kleiber’s rule initiated the use of allometric equations, or power functions of mass, in physiology.