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 amount remaining in the lungs even after the deepest exhalation (i.e. the minimum amount of air remaining in the lungs).

Question

a) 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)=Acos(Bt)+C where V is the volume in mL, t is the time in seconds, and the time t=0 corresponds to the lungs being at their fullest.

Answer 1

I think it may be:
V(t)=1600cos(pi x t)+1150

But a previous tutor said the "+1150" was incorrect on this website so I am not sure.

Answer 2

**RESOLVED**

For any future calculus students who get stumped with this (relatively simple) problem:

You must have 1150 mL of air in your lungs AT MINIMUM. That means at your local minimum in your cos graph the y-value must be 1150, which makes the last part of your equation (C) to be "+2750" not "+1150".

Therefore the final equation is:

V(t)=1600cos(pi x t)+2750