# Is the function f(x) = (2/3)^x increasing or decreasing?

Jun 5, 2018

Decreasing

#### Explanation:

This is an exponential function where the number in the parentheses is the growth factor. Since the absolute value of the growth factor is between 0 and 1, it is a decreasing function.

In other words this means that every time x goes up by 1, the next number is the previous term multiplied by $\frac{2}{3}$.

Here are the first 5 numbers in the sequence starting at the 0th term:
$1 , \frac{2}{3} , \frac{4}{9} , \frac{8}{27} , \frac{16}{81.} . .$

Clearly this sequence is decreasing exponentially.