In a normal respiratory cycle the volume of air that moves i

In a normal respiratory cycle the volume of air that moves into and out of the lungs is about 500 mL. The reserve and residual volumes of air that remain in the lungs occupy about 2000 mL and a single respiratory cycle for an average human takes about 4 seconds. Find a model for the total volume of air V (t) in the lungs as a function of time. Assume that at time t = 0, the lung is at residual volume.

Solution

Given that situation is of cyclic function of 4 seconds or you can also say periodic with 4 seconds.
We know that sin or cos is a periodic function so we can use one of them.
Let\'s use Sin function to create the model.
given period
Given that total reserve volume = 2000mL
volume which circulates = 500mL

then total volume is given by
V(t) = reserved volume + cycle volme = 2000+ 500 sin(kt)

where k is the frequency = 2pi/T = 2pi/4 = pi/2
then final answer is given by
V(t) = 2000+ 500 sin(p/2)t