The exponential e is used when modeling continuous growth that occurs naturally such as populations, bacteria, radioactive decay, etc.
Step-by-step explanation
We can think of e like a universal constant representing how fast we could possibly grow using a continuous process. And, the beauty of e is that not only is it used to represent continuous growth, but it can also represent growth measured periodically across time.
The exponential e will be used in situations of continuous growth or decay. The following formula is used to illustrate continuous growth and decay. If a quantity grows continuously by a fixed percent, the pattern can be depicted by this function.
In case of exponential decay, k is less than 0.