> For the complete documentation index, see [llms.txt](https://101.warmersun.com/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://101.warmersun.com/introduction/characteristics-of-exponential-functions.md).

# Characteristics of Exponential Functions

we call functions like this "exponential" because *x* is in the exponent

![](https://s3.amazonaws.com/img.courses.warmersun.com/progressandpredictions/Slide2.PNG)

## 1% or 10% or 100% interest… does it change the picture?

When you put your money in the bank… of course it matters.

In the big scheme of things there is no difference as long as we take a number greater than one and keep multiplying it with itself repeatedly we see a similar curve:

![](https://s3.amazonaws.com/img.courses.warmersun.com/progressandpredictions/expmultiplecompared.png)

## Slow exponential growth is sub-linear

![in other words: the straight green line (linear) is above the blue (exponential) curve](https://s3.amazonaws.com/img.courses.warmersun.com/progressandpredictions/sublinearexp.png)