Yes, a line of best fit has to be a line which is just a short way of saying straight line. All lines are straight!
Yes, your line of best fit does have to be a line. HOWEVER, since your data looks logarithmic, then a logarithmic transformation to the data would be appropriate to make your data linear.
Note that the model might be appropriate. If we let , this gives , a LINEAR function.
So what you can do is to evaluate for each of your observed x values, and then do a least squares linear regression on the two sets and . Your model will then be much more accurate, and then it can be written in terms of again.