# Question #0ec8d

Jun 20, 2017

$f \left(x\right) = {2}^{x}$

#### Explanation:

Each number in the sequence is the result of 2 raised to a positive integer. If the function is further defined to only include positive integers, the sequence shown can be explicitly defined.

$f \left(x\right) = {2}^{x}$ such that $x \in \mathbb{Z}$ and $0 < x < 6$.

Plugging into this formula with the given conditions, it can be seen that the explicit formula defines the sequence:

$f \left(1\right) = {2}^{1} = 2$
$f \left(2\right) = {2}^{2} = 4$
$f \left(3\right) = {2}^{3} = 8$
$f \left(4\right) = {2}^{4} = 16$
$f \left(5\right) = {2}^{5} = 32$