Repeat Exercise 39 with the inspiration rate function R(t) = −1.2t³ + 5.72t liters/sec and sketch the graph of R(t).

Data from Exercises 39

A pneumotachograph is a device used by physicians to graph the rate of air flow into and out of the lungs as a patient breathes. The graph in the accompanying figure shows the rate of inspiration (breathing in) for a particular patient. The area under the graph measures the total volume of air inhaled by the patient during the inspiration phase of one breathing cycle. Assume the inspiration rate is given by R(t) = −0.41t² + 0.97t liters/sec

a. How long is the inspiration phase?

b. Find the volume of air taken into the patient’s lungs during the inspiration phase.

c. What is the average flow rate of air into the lungs during the inspiration phase?

0.5 R (liters/sec) R= -0.412 +0.97t 1 2 + -t (sec) 3