Definitely exponential. If this function were linear, then the slope, based upon the 1st two points, would be 4; the function would be y-8 = 4(x-2), or
y = 8 + 4x - 8, or y = 4x. Then, if x = 4, y would be 4(4), or 16. This is very different from the point (4, 128) given in the table.
The exponential function in question has a first value of 2 and a common ratio of 4.