The volume of air in a person's lungs can be modeled with a periodic function. The graph below represents the volume of air, in mL, in a person's lungs over time t, measured in seconds.
What is the period and what does it represent in this context?
0
Time (in seconds)
Volume of air (in mL)
t
v
0
Time (in seconds)
Volume of air (in mL)
(2.25, 2100)
(7.25, 2100)
(4.75, 1100)
(9.75, 1100)
The period of the function is the time it takes for the graph to complete one full cycle. In this context, the period represents the time it takes for the volume of air in a person's lungs to repeat its pattern.
To find the period, we can look at the x-values where the graph repeats its pattern. From the given data points, we can see that the volume oscillates between 2100 mL and 1100 mL.
Looking at the x-values, we can see that the pattern repeats every 5 seconds (4.75 - 2.25 = 2.5 and 9.75 - 7.25 = 2.5). Therefore, the period of the function is 5 seconds.