Breathing is cyclic and a full respiratory cycle from the beginning of inhalatio

Question

Breathing is cyclic and a full respiratory cycle from the beginning of inhalation to the end of exhalation takes about 5 seconds. The maximum rate of air flow into the lungs is about 0.5 L/s. This explains, in part, why the function f(t)=1/2sin(2t/5) has often been used to model the rate of air flow into the lungs. This can then be used to show that the volume of inhaled air in the lungs at time t is given by V(t)=5/4[1cos((2/5)t)] liters. Use this to compute the average volume (in liters) of inhaled air in the lungs in one respiratory cycle.

Explanation / Answer

find when the volume function is maximized
solve for when f[t] = 0
f[t] is zero at t=2.5
plug that into V[t]
obtain 7.853L
divide by the time 5s because it takes twice the time to inhale then exhale
obtain Pi/2 Liters

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