Mathematical modelings are used to represent the real problem situations in mathematical concepts. It is used in almost every field, natural sciences, engineering disciplines, social sciences etc.

Mathematical modeling is done by analyzing a problem, formulating it and computing solutions and hence validating the results.

It helps in describing about different systems and effects of different components, to make predictions regarding the behavior, to make estimations about real life events, etc.

Examples:

1. Cost of taxi drive.

Suppose that for a taxi ride, there is a service charge of $9 and another charge of $0.25 per mile for the trip. If x is the number of miles travelled and y is the cost of the taxi ride, then the linear equation for the cost will be,

\(y = 0.25\ \times\ 49\)

2. Dimensions of a plot.

The area of a rectangular plot is 1.00cm. The width of the plot is twice its length. Then, the dimensions of the plot can be obtained.

Consider l as the length of the plot and w as the width of the plot.

Then, \(w = 2l\) and the following equation is formulated.

\(l\ \times\ 2l = 100\ cm^{2}\)

On solving the above equation, the dimensions of the plot can be obtained.