What Are Linear and Exponential Functions?

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A linear function is graphed as a straight line and contains one independent variable and one dependent variable, whereas an exponential function has a rapid increase or decrease along a curved line in a graph. Linear functions, or equations, take the form “y = a + bx,” in which “x” is the dependent variable that changes with the value of “b.” The simplest exponential function is “y = 2^x.”

Linear functions are used in economics and business to calculate expenditures, revenues and profits. For example, the overall profit can be expressed as a linear equation based upon the revenue minus the cost of units sold. For example, consider a bookstore that spent $2 per book to stock the item and sold the book for $5. The linear equation for the bookstore’s profit would be “y=5x-2z,” where y is the total profit, x is the total number of units sold and z is the total number of units bought.

Exponential functions change more rapidly than linear functions. Instead of a gradual rate, every time the exponential variable increases, the effect is multiplied several times instead of added. Two squared is four, two cubed is eight and two to the fourth power is 16. In an exponential equation with two as the base, every variable increase doubles the previous figure. Instead of a gradual straight line, the graph of an exponential function goes upward or downward very quickly.