# Understand Exponential Function in Machine Learning – Machine Learning Tutorial

By | June 9, 2021

Exponential function is defined as:

$$y = a^x$$ where $$a >0$$ and $$a \neq 0$$.

This kind of function is widely used in machine learning. In this tutorial, we will introduce some important features when using it.

Look at image below:

1. if $$a<1$$, $$b < 1$$ and $$a < b$$.

if $$x > 0$$, then $$a^x < b^x$$

Here is an example:

$$(\frac{1}{2})^{x_0}>(\frac{1}{3})^{x_0}$$

if $$x < 0$$, then $$a^x > b^x$$

$$(\frac{1}{2})^{x_0}<(\frac{1}{3})^{x_0}$$

2. if $$a>1$$, $$b >1$$ and $$a < b$$.

if $$x > 0$$, then $$a^x < b^x$$

$$2^{x_0}<3^{x_0}$$

if $$x < 0$$, then $$a^x > b^x$$

$$2^{x_0}>3^{x_0}$$

In machine learning, decay function may use these feature. Here is an example:

If $$\lambda$$ is given. Different $$\frac{L-i+t}{L}$$ will get different value.