An exponential model would work best. There is no constant rate of increase, ruling out a linear model. Additionally, there is not increasing-decreasing trend between the y values, ruling out a quadratic model. There is a considerable increase in the units it takes to transition from one unit of x to another unit of x. For example, going from x = 1 to x = 2, it takes 16.5 units. However, when going from x = 2 to x = 3, it takes 27.5 units. This difference in numbers keeps increasing exponentially, not at a constant rate, therefore an exponential model would work best.
