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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:

f(x)=a*b^x

the domain of which is the set of real numbers \mathbb{R}.
Its codomain is the set of non-negative real numbers \mathbbR_+.

Both a and b must be non-negative numbers.

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

FV=PV*(1+r)^n

Draw the graph of an exponential function

Please enter the values of a and b of an exponential funtion of the form
f(x)=a*b^x
and select the maximum and minimum of the input interval.

a: 
b: 
min. x: 
max. x: 

The constant ratio b

b in the function f(x)=a*b^x 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:

b=sqrt[x_2-x_1]{frac{y_2}{y_1}}

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:

a=frac{y_1}{b^{x_1}}

Calculate a and b with two points given.

Please enter the coordinates of two points.

Point 1
x1: y1:
Point 2
x2: y2:

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.