I have a set of data that contains an ordered pair of (x,y) values. The data, when plotted, is a curve with one peak, as seen below. I modelled the tail of the data with a power and exponential function, as seen below. Both fits were calculated so that the chi squared value is a minimum. The exponential fit is of the form $y = A_1 e^{B_1x}$, and power fit is of the form $y = A_2x^{B_2}$.
I am confused as to why both models fit the data very well. The reason for my confusion is that an exponential function is of a very different form than a power function, yet the data is represented by both functions very well.
Edit: The difference of the exponential fit and power fit looks like the following: 