The model, as written, is non-linear. But it is pointless to think of a model that way. The only thing you've done by fitting a model that way is (i) complicated things and (ii) forced the relationship between the response and predictor to be positive. You would be better off fitting a model where you set , which would be linear and remove the imposed restriction. If you can get, you want the model to be linear. You typically would only fit a non-linear model if there wasn't any way you could make it linear. For example, if you want to fit the model , you could do that by fitting the model instead.

As for determining what predictors are statistically significant, you probably should read a textbook or take a course in this material. It would also clear up any misunderstandings you have. Regression is, at the very least, a semester long undergraduate course that typically focuses 90% on Linear Regression, and has at least a semester of background material as a prerequisite that you've hopefully already had. I really can't answer that question succinctly well given where you are, and even if I could, I would risk causing you to screw up whatever you are doing, since the correct thing to do in a Regression setting often depends on technical details. That is, I think it would be best for you if I didn't answer that question, and just direct you to a textbook. I can post some course notes if you want.