I assume by 'other' functions you mean 'linear' functions. The biggest difference between exponential and linear functions is that linear functions change at a constant rate, while exponential functions change at a rate proportional to it's value, or exponent.
Basically, that's also what separates exponential functions from all others. It's the only function that changes at a rate proportional to its exponent.
In an exponential function, the base is fixed, and the independent variable is in the exponent. This is different from previous functions we have studied, where the exponent was a fixed number and the base varied.
