Having a lot of trouble with this one:
Q) Tidal volume is the volume of air displaced in the lungs between inhalation and exhalation (the amount of air in a breath). The residual volume is given by the remaining in the lungs even after the deepest exhalation (ie the minimum amount of air remaining in the lungs).
Suppose that a person is running and a full breath is completed every 2 seconds. Further suppose that the person’s tidal volume during the run is 3200 mL and that the residual volume is 1150 mL. Express the volume of air in the person’s lungs in the form V (t) = A cos (Bt) + C where V is the volume in millilitres, t isthe time in seconds, and the time t = 0 corresponds to the lungs being at their fullest.
Suppose a person were to breath an average of 12 times per minute.
How many hours would it take for them to breathe one billion times?
To express the volume of air in the person's lungs in the given form V(t) = A cos(Bt) + C, we need to determine the values of A, B, and C based on the given information.
We know that the tidal volume during the run is 3200 mL, so A should be equal to 3200. This means the amplitude of the cosine function will be 3200.
The residual volume is given as 1150 mL, which means that when the lungs are at their emptiest, there will still be 1150 mL of air. Since the amplitude of the cosine function represents the maximum deviation from the equilibrium position, C should be equal to the residual volume, i.e., C = 1150.
Now, let's consider the time component. We are told that a full breath is completed every 2 seconds. This gives us the period of the function, which is the time it takes for one complete cycle of the cosine function. In this case, the period is 2 seconds, which means that B should be equal to 2π divided by the period, B = 2π/2 = π.
Therefore, the volume of air in the person's lungs can be expressed as V(t) = 3200 cos(πt) + 1150, where V is the volume in millilitres and t is the time in seconds.