Applications Of Functions

Functions arise in a great variety of situations. Here are some examples.

Geometry:

• πr² = area of a circle of radius r
• 4πr² = surface area of a sphere of radius r
• 4/3πr³ = volume of a sphere of radius
• r sin θ = the sine of the angle θ

Physics:

• s(t) = distance a particle travels from time 0 to t
• v(t) = velocity of a particle at time t
• a(t) = acceleration of a particle at time t
• p(y) = water pressure at depth y below the surface
• C = 5/9(F - 32) = Celsius temperature as a function of Fahrenheit temperature

Economics:

• f(t) = population at time t
• p(t) = price of a commodity at time t
• c(x) = cost of x items of a commodity
• D(p) = demand for a commodity at price p, i.e., the amount which can be sold at price p

Functions of two or more variables can be dealt with in a similar way. Here is the precise definition of a function of two variables.