model for an exponential function

I am struggling with an exponential kind of function (it's stock market so not a function itself). It's the function of bitcoin basically. As you can see it's exponential-like increasing since 2011.

Now I don't give this example for price prediction but for genuine interest in statistics. Well what the difference between a logaritmic model and an expnential model?

Because both seem pretty much the same in the shape of the line which fits the data.

2) question: Let's assume that my regression linear model explain an exponential function the better than a logaritmic/exponential model itself... well in this case... what do you do generally? Is it a strange case orrr not? A linear fits better than an exponential model for the last part of the curve (the one where the expon. curve is flattening).

Well in this case... what to do? Why to use the exponential model and not the linear since the last part of the function / stock is predicted better by the linear model?


No cake for spunky
Personally I would use a model that predicts better if that is what you are asking about. But if you violate the assumptions of the model then your p values won't be accurate (or might not be). And just because it works with one sample does not mean it will in the future with other ones.