Which term represents a formal acknowledgment of something?

The term that represents a formal acknowledgment of something is "apprise." To apprise someone means to inform or notify them formally regarding a particular fact or situation. This word emphasizes the act of providing important information and ensuring understanding. In formal contexts, being apprised of something indicates that the acknowledgment is not only made but is also recognized as significant.

The other terms—"appropriation"—typically refers to the act of taking something for one's own use, often without permission or a formal acknowledgment attached to it. Here, it does not convey the notion of recognizing or formally acknowledging something. Thus, "apprise" is the correct term as it aligns with the idea of formal acknowledgment.