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Exponential Function

An exponential function is a nonlinear function that can be written in the following form, where and As the independent variable changes by a constant amount, the dependent variable multiplied by a constant factor. Therefore, consecutive values form a constant ratio.

Here, the coefficient is the intercept, which is sometimes referred to as the initial value. The base can be interpreted as the constant factor. The graph of an exponential function depends on the values of and
Graph of y=a*b^x for a-values less than and greater than 0, and for b-values less than and greater than 1.


If the coefficient is the function becomes a horizontal line.
This is a line along the axis and, therefore, is a linear relation. This means that if then the function is not exponential.
Graph of y=a*2^x where the value of 'a' can be changed from -2.5 to 2.5


Why and
If the base is negative, the function gives undefined results for certain values. For example, since a negative value for would yield non-real values for Hence, a condition on is needed.
However, if or , the function becomes a horizontal line.
Therefore, cannot be equal to nor
Graph of y=2*b^x where the value of 'b' can be changed from 0.1 to 2