How to understand the word "exponent"? I have some difficulty in understanding the complex exponential function. So I decide to review the good old exponent function which I learned long ago.
I look up the word exponent, the online dictionary says this:

noun
  
  
*
  
*a person or thing that expounds, explains, or interprets: an exponent of modern theory in the arts.
  
*a person or thing that is a representative, advocate, type, or symbol of something: Lincoln is an exponent of American democracy.
  
*Mathematics. a symbol or number placed above and after another symbol or number to denote the power to which the latter is to be
  raised: The exponents of the quantities xn, 2m, y 4 , and 3 5 are,
  respectively, n, m, 4, and 5.
  

I am not a native English speaker. To me, these 3 meanings are so distinct. Why are they sharing the same word exponent? I think the subtle relations among these 3 meanings may help me better understand the human rationale/subconsciousness behind the mathematical concept.
ADD 1
According to here, the exponent part is also called index, or power. I think the latter ones are more acceptable.

 A: You are not the first to ask that question (perhaps in the stackexchange network you do).
Googling a bit: http://mathforum.org/library/drmath/view/65184.html

Looking up the context of this sentence in Smith, I find that it 
  follows a table of powers of 2:
0   1   2   3   4   5   6   7   8 
1   2   4   8  16  32  64  128 256

He says (in Latin), "Just as, by addition, (in the upper row) 3 
  [added] to 5 makes 8, so (in the bottom row), by multiplication, 8 
  [multiplied] by 32 makes 256".  [...] So the words "exponent" refers to > the number in the top row 
  corresponding to a given number in the bottom row; this is the number 
  of 2's multiplied to make the given number--what we today would  call
  its base-2 logarithm, or the exponent of 2 that gives the number.

In short, it's impossible to know the exact meaning or reason of choosing exponent instead of any other word. I don't think you'll be able of deducing the intrinsics of Smith's mind from their explanations when choosing exponent, because he died five centuries ago.
A: The common thread in the three definitions is that an exponent is something which increases or highlights a thing.   To make something larger, or more clear.

1.a person or thing that expounds, explains, or interprets: an exponent of modern theory in the arts.

They are people or things which seek to increase or highlight knowledge.

2.a person or thing that is a representative, advocate, type, or symbol of something: Lincoln is an exponent of American democracy.

They are people or things which seek to increase or highlight principles; by example or through leadership.

3.Mathematics. a symbol or number placed above and after another symbol or number to denote the power to which the latter is to be raised: The exponents of the quantities $x^n, 2^m, y^4$ , and $3^5$ are, respectively, $n, m, 4,$ and $5$.

They are things (mathematical operations) which increase the values.   Albeit, in mathematical usage an exponent may perhaps do so negatively, depending.
