Functions describe situations where one quantity determines another. For example, the return of $10,000 invested at an interest rate of 4.25% per year is a function of the number of years the money is invested. Because they help investigate the dependencies between quantities in nature and society, functions are important tools in constructing mathematical models.

In school mathematics, functions usually have numerical inputs and outputs and are often defined by an algebraic expression. For example, the time in hours it takes for a car to drive 100 miles is a function of the car's speed in miles per hour, v. The rule T(v)= 100/v expresses this relationship algebraically and defines a function whose name is T.

A very current example of the connection between mathemtical functions and real life situation is the recent Covid Pandemic.
The algebraic expression modeling the number of infections in a population is an exponential function depending on many variables including time, the number of people in the whole population, the number of people already infected and the rate of transmission.

Exponential Growth Video

Exponential Growth Graph

Covid: Math Rule and Table