There are some issues with your fit. First, log(0) is not defined, so what you expect to become from a fit that uses log(0)? If you really want to use this point to a logarithmic fit you have to make some consideration like calculating log(x+eps) instead of log(x), although this will unlikely lead to a reasonable model. Second, what type of function you think you have? The second y value has a way higher value than all others, it is an outlier/measurement error that needs to be removed? Or you are modelling a probability function and there is the peak? If so, why use a 1 degree exponential function and not a probability function such as a gaussian to model it?
If you don't define what type of model you're expecting to have it doesn't make much sense to make a fit on it.
