The total amount of air in our langs as we breathe in and out can be modeled by a sinusoidal function. An average relaxed adult male breathes (in and out about 15 times per minute, cach time breathing in and out about 500mL of air. At the end of exhalation, about 2400 mL e air remain in the lungs Let -MCdenote the volume (in mb) of air in the lungs seconds afher inhalation begins a. Sketch a graph of V =M() for OSISI Be sure to label your axes and label the coordinates of the key points. b. Sute the period, amplitude and midline of MCO). Be sure to include units. Period Amplitude Midline c. An average adult female also breathes in about 15 times per minute, but both the amount of air she breathes in and out and the amount of air remaining in her lungs after exhalation are about 22% less than that of the average male. Let 4 = F(!) denote the volume (in ml) of air in the lungs of an average female seconds after inhalation begins. Find the period, amplitude, and midline of Fil). Midline Period Amplitude d. Find a formula for Fun in terms of Min. FC) e. A student whose breathing is modeled by M) is about to take an exam. He consciously decides to slow down his breathing, to about 10 breaths per minute instead of 15. He inhales more deeply and exhales more fully. When he does this, the average amount of air in his lungs stays the same even though the amount of air that he is breathing in and out increases by about 2016 Let Rio denote the volume of air in his lungs seconds after he begins inhaling in this new way Note that is still a sinusoidal function Express Rain in terms of MO. RE)