Functions

Abstract

This project investigates how calculus specifically the study of exponential functions, derivatives, limits, and integrals can be applied to model the concentration of a drug in the human bloodstream over time. Using Ibuprofen as a case study, we define a mathematical function f(t) = D \cdot e^{-kt}, compute its derivative to analyze the rate of drug elimination, evaluate limits to determine long-term behavior, and use definite integrals to calculate total drug exposure. The results are interpreted within the clinical concept of the therapeutic window to demonstrate why doctors prescribe specific dosages and time intervals.

Research Team