What's the relationship between compound interest and exponential growth?

 I would say that compound interest is a form of exponential growth. 
the exponential functions are the family of functions that have the form a^x, where a > 1. 
Compound interest is modeled as an exponentila growth problem. Another phenomenon that can be modeled as exponential growth is population growth. 
In other words, compound interest is an application of exponential growth.