Is it more accurate to use the term Geometric Growth or Exponential Growth? On Wikipedia, the terms Exponential Growth and Geometric Growth are listed as synonymous, and defined as when the growth rate of the value of a mathematical function is proportional to the function's current value but I question whether one term is more mathematically correct than the other?  For example, there is a Geometric Progression but no Exponential Progression article on Wikipedia, so perhaps the term Geometric is a bit more accurate, mathematically speaking?  Why are there two terms for this type of growth?  Perhaps exponential growth is more popular in common parlance, and geometric in mathematical circles?
In my 50 or so years of studying mathematics, I've never encountered "geometric growth", but often have met "exponential growth". So that's one small bit of evidence that if you want to sound like most mathematicians, you should use "exponential growth." I wouldn't say either is "more mathematically correct," for the assignment of words as names for concepts is not one that's subject to mathematical evaluation. (Is "continuous" really the right word for the thing we call continuity? Perhaps not...consider a function like 
$$
f(x)= \begin{cases}
\frac{1}{2^k} &amp; \text{ if $x = \frac{p}{2^k}$ in lowest terms} \\
0 &amp; \text{otherwise}
\end{cases}
$$
which is continuous at every irrational, and at no rational. But if you used any term other than "continuous" for this thing, mathematicians would regard it as somewhere between "peculiar" and "redundant" and "wrong" :) . )
Wow! I can't believe I'm in this discussion. I am NOT any kind of mathematician. But I thought that it worked like this: 

Geometric: a number is multiplied by a fixed factor, and then the product is multiplied by that same fixed factor... etc. For example:
$$1\times1.2=1.2$$
$$1.2\times1.2=1.44$$
$$1.44\times1.2=1.728$$
$$1.728\times1.2=2.0736$$

Exponential: a number is multiplied by a factor that, instead of being fixed, grows  as the succeeding products grow; i.e., the factor is in proportion to each product. For example:
$$1\times1.2=1.2$$
$$1.2\times(1.2\times1.2)=1.728$$
$$1.728\times(1.728\times1.2)=3.583$$
$$3.583\times(3.583\times1.2)=15.405$$