$\Large f(n)= \left \lfloor 2^{n+\frac{3}{2}} \right \rfloor - 2 \left \lfloor 2^{n+\frac{1}{2}} \right \rfloor$

The above function is defined on the natural numbers. Which of the following describes the periodicity of the function?

- A. Eventually periodic with period in $[1,10^3)$.
- B. Eventually periodic with period in $[10^3,10^6)$.
- C. Eventually periodic with period in $[10^6,\infty)$.
- D. Not eventually periodic.