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:
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 (x1, y1) and (x2, y2) 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 (x1, y1) of the graph and the constant radio b is given:
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.