Appropriate is a very good and safe word in a professional setting. If you use it, you are saying it's a model that will do a good job in this application.
I would suggest some other synonyms, but I am not able to understand some of your other language. You have some serious problems. For example, extend is a verb, not an adjective that can be applied to a model. Extent is a similar word, but it's a noun. You need to replace this word with one that makes sense in your context.
It sounds like this is a theoretical model. But you use the words big and small, which are normally reserved for physical objects.
In order to help you we need more information: Is this model a physical object or a theory? What is it about this model that would make it appropriate or inappropriate for your application? It's size? Complexity?