On average, the lung of human male human holds 6 liters of air at maximum inhala

Question

On average, the lung of human male human holds 6 liters of air at maximum inhalation and 1 liter at maximum exhalation. Assume that the volume of air in his lung varies sinusoidally with time as he breathes in and out. Find an expression that models the volume, V, of air (in liters) in the lung of a typical man at a time t (in seconds) if he is taking deep breaths each minute. Include units in the variables of the formula For example, t = 30 sec, not t = 30, must be used in the formula to determine the volume at t = 30 sec.

Explanation / Answer

Inhalation = 6 L
Exhalation = 1 L

So, max = 6
and min = 1

A = amplitude = (max - min)/2
A = (6 - 1)/2
A = 2.5

D = vertical shift = (max + min)/2
D = 7/2
D = 3.5

15 breaths in 60 seconds...

So, 1 breath in 4 seconds

So, period = 4

And thus, B = 2pi/4 = pi/2

So, we have :
y = Asin[B(x - C)] + D

y = 2.5sin(pi*x/2) + 3.5 -----> ANSWER

x is in seconds

And y is in Liters

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