Relating mathematics learned in the classroom to real situations increases student motivation and enhances learning. In this paper, we provide an example of a classroom application of calculus to physiology in two courses: "Differential Equations" and "Calculus I for Biology and Medicine." We designed and implemented a project that uses calculus to model the volume, flow, and pressure of air inside the lungs of a patient receiving positive pressure ventilation. After comparing mathematical models to a mechanically ventilated high-fidelity breathing simulator, students reported heightened interest in, and a greater appreciation for, the relevance of the calculus in both courses.