The volume of air in the lungs during normal breathing is a sinusoidal function of time given by: I' =300 sin ~f + 2500 , where tis the time in seconds and is in ml. 2 a) Find the average rate of change of the volume during the first 1.5 seconds. b) Estimate the instantaneous rate of change of volume at seconds. What does this tell you about the breathing at this time? c) Describe how the original graph would change if : (i) the person breathes more rapidly (ii) the person takes bigger breaths