Answer
The function is an exponential function with a common ratio of $\dfrac{1}{2}$.
$F (x)=(\dfrac{1}{2})^{x+2}$.
Work Step by Step
We can see that the ratio of consecutive vales is fixed or constant.
That is, $\dfrac{1/4}{1/2}=\dfrac{1/8}{1/4}=\dfrac{1/16}{1/8}=\dfrac{1/32}{1/16}=\dfrac{1}{2}$
Thus, the function is an exponential function with a common ratio of $\dfrac{1}{2}$.
The difference of consecutive vales is not fixed or constant.
That is, $\dfrac{1}{4}-\dfrac{1}{8} \ne \dfrac{1}{2}-\dfrac{1}{4}$
Thus, the function is not a linear function.
So, we conclude that the function has a common ratio of $\dfrac{1}{2}$, $F (0)=(\dfrac{1}{2})^2$, and can be modeled with
$F (x)=(\dfrac{1}{2})^{x+2}$.
