Cheyne-Stokes Respiration, a respiratory ailment, causes the volume per breath to increase and decrease as a function of time, and this change can be modeled by a sinusoidal function. A machine is used to record 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 . During a test, the smallest volume per breath is 0.6 liters and this occurs 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?