# Exponential function

The variable x of an exponential function x is in the exponent. An exponential function can be used to exhibit exponential growth or decay.

The basic exponential functions form is given by:

the domain of which is the set of real numbers .

Its codomain is the set of non-negative real numbers .

Both a and b must be non-negative numbers.

The formula for the future value of capital is an example of an exponential function:

## Draw the graph of an exponential function

Please enter the values of a and b of an exponential funtion of the formand select the maximum and minimum of the input interval.

## The constant ratio b

b in the function is known as the base or the constant ratio. It indicates how fast the function f(x) grows or decays.

b > 1 : the graph increases (exponential growth)

b < 1 : the graph deacreases (exponential decay)

The constant ratio b can be calculated, if two points (x_{1}, y_{1}) and (x_{2}, y_{2}) of the funtions graph are given:

## The leading coefficient a

a is the leading coefficient. It indicates the graph’s intersection with the y-axis in the point (0,a).

The leading coefficient can be calculated, if on point (x_{1}, y_{1}) of the graph and the constant radio b is given:

## Calculate a and b with two points given.

Please enter the coordinates of two points.## Recognizing an exponential trend in a data set

If you have a data sets and you want to know if there is an exponetial relationship between them, you can plot them in a coordinate system with logarithmic scale on the y-axis.

The more the points fit to a straight line, the closer to an exponential trend the data are.