Question

1. the volume of air in a persons lungs can be mode with a periodic function. the graph below represents the volume of air, in ml, in a persons lungs over time t, measured in seconds. what is the period and what does it represent in this context? the period is ____ __ and it represents ____. word bank 1: (a) ml, (b) seconds word bank 2: (a) the average air volume, (b) the time between consecutive peaks in air volume, (c) how often the breathing cycle repeats in a second, (d) the difference between maximum and minimum air volume

Explanation:

Step1: Calculate the period

The period of a periodic function is the horizontal length between two consecutive peaks (or troughs).
The \(x\) - values of two consecutive peaks are \(t = 1.25\) and \(t=4.25\).
The period \(P=4.25 - 1.25\)

$$P = 3$$

Step2: Interpret the period

In the context of the volume of air in the lungs over time, the period represents the time it takes for the breathing cycle (inhaling and exhaling) to repeat.

Answer:

The period is \(3\) seconds and it represents the time between consecutive peaks in air volume.