# What is an example of a value of b for which y=b^x represents an exponential decay?

Nov 9, 2016

Any $b \in \left(0 , 1\right)$

#### Explanation:

With $b > 0 , {b}^{x} > 0$ and

$y = {b}^{x}$ represents decay for b < 1.

Proof:

y'=b^x/ln b < 0, as ln b < 0.

So, y is a decreasing function.

Example:

$\left(x , {\left(0.1\right)}^{x}\right) \ldots : \left(- 2 , 100\right) \left(- 1 , 10\right) \left(0 , 1\right) \left(1 , 0.1\right) \left(2 , 0.01\right) \ldots$