"Its just a math equation": Examining resource coordination in physics students� reasoning about exponential functions and drag

Exponential functions are foundational to modeling dynamic phenomena in physics, yet students often struggle to integrate their mathematical form with corresponding physical interpretations.This study reports on upper-division physics students' reasoning about exponential decay in the context of projectile motion with drag.Using the knowledge in pieces framework, we analyze how students activate and coordinate mathematical and conceptual resources during problem-solving.Case studies reveal that while participants demonstrated procedural fluency with exponential expressions, they did not construe these forms as meaningful representations of physical systems.In contrast, polynomial forms elicited stronger conceptual associations, suggesting that curricular familiarity plays a role in resource coordination.These findings underscore a persistent disconnect between symbolic manipulation and physical interpretation in students' reasoning.We argue for instructional designs that explicitly foster connections between mathematical structure (e.g., e -kt ) and mechanistic models (e.g., velocity-dependent drag), thereby supporting more integrated and expert-like engagement with exponential functions in physics contexts.