An exponential function is one that has the variable in the exponent of an algebraic expression.
[tex]f(x)=a^{(x+c)}[/tex]
is an exponential function. The base (a) does not need to be a constant, but usually is for the functions we study. The exponent here is a linear function of x, but can be any* function of x, including another exponential function.
The number of forms of exponential functions that we can solve is somewhat limited, so our study is usually restricted to those forms. For example, in general, we cannot use algebraic methods to solve equations that involve sums of polynomial and exponential functions, such as ...
[tex]e^{x}+x-3=0[/tex]
___
* if the exponent is a log function, simplification may result in something that is not actually an exponential function. For example, e^(ln(x)) = x, a linear function.
