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In a normal respiratory cycle the volume of air that moves into and out of  the lungs is about 500 mL. The reserve and residual volumes of air th at  remain in the lungs occupy about  2000mL and a single respiratory cycle for  an average human takes about 4 seconds. Find a model for the total volume of air V(t) in the lungs as a function of time.Help! My homework is due really soon and I can't figure it out!  My book is called Biocalculus: Calculus for Life Sciences.

Question

In a normal respiratory cycle the volume of air that moves into and out of  the lungs is about 500 mL. The reserve and residual volumes of air th at  remain in the lungs occupy about  2000mL and a single respiratory cycle for  an average human takes about 4 seconds. Find a model for the total volume of air V(t) in the lungs as a function of time.

Help! My homework is due really soon and I can't figure it out!  My book is called Biocalculus: Calculus for Life Sciences.

check_circleAnswer
Step 1

The volume of air that is coming in and going out is 500ml. A single respiratory cycle takes 4 seconds to complete. The residual volume of air left in the lung after the completion of the cycle is 2000 ml.

Step 2

At t = 0,  V ( t) = 2000. As it takes 4 seconds to complete the complete the cycle, assume that it takes 2 seconds by air to come in and 2 seconds to go out. That means at t = 2, V(2) = 2000+500 = 2500 and at t = 4,  V(4) = 2500-500 = 2000. Try to find the volume of air at 1 and 3 seconds.

At 1 second, the half of the coming in volume of air enters the lungs.

Thus, V(1) = 2000+250 = 2250.

At 3 second, the half of the going out volume of air leaves the lungs.

Step 3

Thus, V(1) = 2500-250 = 2250. Thus, the single...

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