Appreciable means large enough to notice or to matter. It almost always goes with amounts, differences, changes, and effects: an appreciable difference, no appreciable risk, an appreciable amount of time. Though actually, it does not mean “you feel thankful” — that is appreciative. And it does not mean “you understand the worth of art” — that is a different use of the verb appreciate. This word is a cool, slightly formal way of saying “enough that you would actually notice.” If the change is tiny, it is not appreciable. You will meet it in reports, science, and careful writing more than in chat.