Problem 19.3. A respiratory ailment called “Cheyne-Stokes Respiration” causes th
ID: 2870883 • Letter: P
Question
Problem 19.3. A respiratory ailment called “Cheyne-Stokes Respiration” causes the vol- ume per breath to increase and decrease in a sinusoidal manner, as a function of time. For one particular patient with this condition, a
machine begins recording a plot of volume per breath versus time (in seconds). Let b(t) be a function of time t that tells us the volume (in liters) of a breath that starts at time t. Dur- ing the test, the smallest volume per breath is 0.6 liters and this first occurs for a breath that starts 5 seconds into the test. The largest volume per breath is 1.8 liters and this first occurs for a breath beginning 55 seconds into the test.
(a) Find a formula for the function b(t) whose graph will model the test data for this patient.
(b) If the patient begins a breath every 5 seconds, what are the breath volumes during the first minute of the test?
Explanation / Answer
average=(0.6+1.8)/2 =1.2
amplitude=1.2-0.6=0.6
half period =55-5=50sec ==>period=100sec
B=2pi/100=pi/50
a)b(t)=1.2-0.6cos((pi/50)*(t-5) )
b)b(5)=0.6,b(10)=0.63,b(15)=0.715,b(20)=0.85,b(25)=1.01,b(30)=1.2,b(35)=1.385,b(40)=1.557,b(45)=1.685,b(50)=1.77,b(55)=1.8,b(60)=,1.77