Chapter 1, Problem 9PS

Blood Pressure The pressure $P$ (in millimeters of mercury) against the walls of the blood vessels of a patient is modeled by

$P=100-20\cos \frac{8\pi t}{3}$

where $t$ is the time (in seconds).

(a) Use a graphing utility to graph the model.

(b) What is the period of the model? What does it represent in the context of the problem?

(c) What is the amplitude of the model? What does it represent in the context of the problem?

(d) If one cycle of this model is equivalent to one heartbeat, what is the pulse of the patient?

(e) A physician wants the patient’s pulse rate to be $64$ beats per minute or less. What should the period be? What should the coefficient of $t$ be?