Question

The pressure P against the walls of the blood vessels of a person is modeled by

P = 100-20 cos (8πt / 3), where t is the time (in seconds). One cycle is equivalent to one heartbeat. What is the person's pulse rate in heartbeats per minute?

Answer 1

The pulse rate is calculated by finding the period of the cosine function, converting it to minutes, and then determining the number of cycles in one minute. For the given equation, the period corresponds to 3/4 seconds, resulting in a pulse rate of 80 heartbeats per minute.

Step-by-step explanation:

The student's question is about calculating the pulse rate in heartbeats per minute using the pressure model given by the equation P = 100 - 20 cos(8πt / 3).

First, we need to determine one full cycle of the cosine function, which corresponds to one heartbeat. The general form of the cosine function is cos(bt), where 2π/b gives the period or the time for one complete cycle. For the function provided, b = 8π/3, so one cycle is 2π / (8π/3) = 3/4 seconds.

To find the pulse rate in heartbeats per minute, we convert the time for one cycle into minutes and then calculate the number of cycles in one minute. This is done by dividing 60 seconds by the time for one cycle (0.75 seconds), which gives us the pulse rate of 80 heartbeats per minute.