Respiratory Rate

The rate at which air is drawn into the lungs, during a respiratory cycle, may be approximate by the equation:

    \[\frac{dV}{dt}=\frac{t\left(2t-5\right)\left(t-5\right)}{20}\,\,\,\,\,L/s, 0\leq t\leq 5\,\,s\]

If, at the start of the respiratory cycle \left(t=0\right) the volume V of air in the lungs is 0.1 L, show that the maximum volume of air contained in the lungs is approximately 1.077 L.

Source: Rosenberg, R.L. (1984). Elementary Calculus: Course Notes. Ottawa, Canada: Holt, Rinehart and Winston. (Exercise 6: Question 3(vi), p. 22)

Author: ascklee

Dr. Lee teaches at the Wee Kim Wee School of Communication and Information at the Nanyang Technological University in Singapore. He founded The Mathematics Digital Library in 2013.

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