Given: The number of daily phone calls between two cities varies jointly as their populations and varies inversely as the square of the distance between them. The above stated model is called as gravity model.
Definition used:
(1) Joint Variation:Joint variation is a variation in which a variable varies direcly as the product of two or more other variables. Thus, the equation y = kxz, is read y varies jointly as x and z.
(2) Inverse Variation: If a situation is described by an equation in the form
Description:
Let the average number of daily phone calls is represented as C and population of two cities are
The distance between two cities be represented as d.
From definition (1), the given "The C between the two cities varies jointly as the product of their population" can be expressed as,
Similarly by the definition (2) the given "The C varies inversely as the as the square of distance" can be expressed as,
Combine the equation (1) and equation (2) as follows.
From equation (3), the given model can be expressed as
In general, the newton's formula for gravitation is
The above formula indicates the gravitational force between two objects in the universe. On comparing the gravitational formula with given model, it is observed to be in similar form of joint variation.
Thus, the given model is called as gravity model.