This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by 4 gives the next term. In other words:
an = a1 * r ^ (n-1)
Now, knowing that a1 = 2, and r = 4
We check
a2 = 2 * 4 ^ (2-1) = 2 * (4 ^ 1) = 8
a3 = 2 * 4 ^ (3-1) = 2 * (4 ^ 2) = 32
a4 = 2 * 4 ^ (4-1) = 2 * (4 ^ 3) = 128
Therefore, this is the geometric function that this sequence fulfills.
