Question

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

Answer 1

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 `2/3`.

Here are the first 5 numbers in the sequence starting at the 0th term:
`1, 2/3, 4/9, 8/27, 16/81...`

Clearly this sequence is decreasing exponentially.