Chapter 6.1, Problem 51E

  Air flow in the lungs A simple model (with different parameters for different people) for the flow of air in and out of the lungs is

$V^{\prime }\left(t\right)=-\frac{\pi }{2}\sin \frac{\pi t}{2},$

 where V(t) (measured in liters) is the volume of air in the lungs at time t ≥ 0, t is measured in seconds, and t = 0 corresponds to a time at which the lungs are full and exhalation begins. Only a fraction of the air in the lungs is exchanged with each breath. The amount that is exchanged is called the tidal volume.

1. a. Find the volume function V assuming V(0) = 6 L.
2. b. What is the breathing rate in breaths/min?
3. c. What i3 the tidal volume and what is the total capacity of the lungs?