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A simple model for the flow of air in and out of the lungs of...

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Calculus

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A simple model for the flow of air in and out of the lungs of a certain mammal is given by the following equation 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 Complete parts a through c below V t sin 2 1 2 A V t V 0 v x dx 0 b OC V t V 0 v t dt V t 13 cos Find the volume function V assuming that V 0 14 L a at 2 Type an exact answer b What is the breathing rate in breaths minute The breathing rate is 15 breaths minute Type an integer or a simplified fraction c What is the tidal volume and what is the total capacity of the lungs The tidal volume is 7 3 2 liter s t OB V 0 V t t v x dx 0 b OD V 0 V t V t dt a

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