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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

In a normal respiratory cycle the volume of air that moves into and out of the lungs is about 500 mL. The reserve and residue volumes of air that remain in the lungs occupy about 2000 mL 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.

To determine

To find: Thefunction to determine the total volume of air V(t) in the lungs in terms of time.

Explanation

Given:

The volume of air that moves in and out of the lungs is about 500 mL.

The volume of the air remaining in the lungs is about 2,000 mL and the average time taken by a human being for 1 respiratory cycle is 4 seconds.

Calculation:

The total volume of air equals the sum of the volume of air moved into lungs, the volume of air that moves out from the lungs and the volume of air remains in the lungs.

The total volume of air=500mL+2,000mL=25,00mL

The average volume of air=(The total volume of air in the lungs+The volume of air remains in the lungs)2=2,500+2,0002=4,5002=2,250

The amplitude of the function=(The total volume of�

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