From your description I would say that both equations are identical. They've merely applied a different nametag to the constant.
If then there is exponential growth. If there is exponential decay (towards zero).
In my book I am given the equation A(t) = Aoe^(kt) (for exponential growth) Where t equals time and k is a constant. However, I saw an equation on another site for compounded interest in which k was replaced by r, the rate of interest. When do you use which equation? And what about exponential decay?
From your description I would say that both equations are identical. They've merely applied a different nametag to the constant.
If then there is exponential growth. If there is exponential decay (towards zero).
The equations are the same. and are constants with dimension 1/TIME. Different fields tend to use different symbols but they all refer to a constant. For example you'll see used as a decay constant in radioactivity. A good book will define it's symbols immediately before/after introducing them.
Whether it's growth or decay depends whether or not there is a minus sign since the constant in the exponent is usually taken to be a positive constant. If it's there then you have decay, if not then it's growth. Below is an example
Radioactive decay is given by the formula where is the number of nuclei at any given time, is the initial number of nuclei (when t=0), is a positive decay constant and is time