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what is the biggest difference between exponential functions and other functions?

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.