Question: A simple model (with different parameters for different people) for the flow of air in and out of the lungs is where V(t) (measured in

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

пt т sin 2 V'(t)

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 in exchanged with each breath. The amount that is exchanged is called the tidal volume.

a. Find and graph the volume function V assuming that V(0) = 6 L.

b. What is the breathing rate in breaths/min?

c. What is the tidal volume and what is the total capacity of the lungs?

t sin 2 V'(t)

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