When a person is breathing normally, the amount of air in their lungs can be modeled with a sinusoidal function. When full, Karen’s lungs hold 2.8 liters of air. When “empty,” her lungs hold 0.6 liters of air. Her brother starts timing her breathing. At t = 2 seconds Karen has exhaled completely and at t = 5 seconds she has completely inhaled. Homework Help ✎
Write an equation to model the amount of air in Karen’s lungs at any time t in seconds, assuming she is breathing normally.
What is the amount of air in Karen’s lungs if she starts holding her breath, 3.5 seconds into the timing?
When is the first time Karen has 2.3 liters of air in her lungs?
Make a sketch. Include a minimum point at (2, 0.6) and a maximum point at (5, 2.8).
amplitude: 0.5(2.8 − 0.6)
period: 2(5 − 2)
horizontal shift: 0.5(5 + 2) using sine
vertical shift: 0.5(0.6 + 2.8)
Let t = 3.5 in your equation from part (a).
Set your equation from part (a) equal to 2.3 and solve for t.