If you plot two quantities against each other with logarithmic axes and they show a linear relationship, this indicates that the two quantities have a power law distribution.

Exponent Operator (^) Used to raise a number to the power of an exponent.

A power law is a relationship in which a relative change in one quantity gives rise to a proportional relative change in the other quantity, independent of the initial size of those quantities.

A power function is a function with a single term that is the product of a real number, a coefficient, and a variable raised to a fixed real number. ( A number that multiplies a variable raised to an exponent is known as a coefficient.) As an example, consider functions for area or volume.

The power law model, also known as the Ostwald de Waele relationship, is used to fit non-Newtonian data across shear rates where there is no evidence of a Newtonian plateau region.

Polymers have a consistency index (m) and a power-law coefficient (n) that describe its general viscosity behavior with respect to changing temperature (T) and shear rate (Ÿ). The consistency index is primarily the relationship between the polymer’s viscosity and temperature.

Basically in a power lay function the exponent is constant, and in an exponential equation x the exponent is the variable x. Both forms of equation share the characteristic of being non-linear in form, although log and ln transformations can make them linear.

In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities: one quantity varies as a power of another.

Both forms look very similar. In exponential functions, a fixed base is raised to a variable exponent. In power functions, however, a variable base is raised to a fixed exponent. The parameter b , called either the exponent or the power, determines the function’s rates of growth or decay.

For variables for which the relationship is some kind of power law, a plot of the logarithms of the variables can help extract information about the power relationship. The slope of a log-log plot gives the power of the relationship, and a straight line is an indication that a definite power relationship exists.

Power relations are relationships in which one person has social-formative power over another, and is able to get the other person to do what they wish (whether by compelling obedience or in some less compulsive and even a more subtle way.

In an inverse relationship, an increase in one quantity leads to a corresponding decrease in the other. Mathematically, this is expressed as y = k/x. For a journey, travel time = distance ÷ speed, which is an inverse relationship with the distance traveled as a constant.