Question

1. blood pressure the function

p = 120 + 30 sin 2πt
models the blood pressure (in millimeters of mercury) for a
person who has a (high) blood pressure of 150/90; t represents
seconds.
(b) how many heartbeats are there each minute?

Explanation:

Step1: Identify the period of the sine function

The general form of a sine function is \( y = A\sin(Bx + C)+D \), and the period \( T \) is given by \( T=\frac{2\pi}{|B|} \). In the function \( P = 120 + 30\sin(2\pi t) \), \( B = 2\pi \). So the period \( T=\frac{2\pi}{2\pi}=1 \) second. This means the blood pressure completes one cycle (one heartbeat) every 1 second.

Step2: Calculate heartbeats per minute

Since there are 60 seconds in a minute, and one heartbeat occurs every 1 second, the number of heartbeats per minute is \( \frac{60}{1}=60 \).

Answer:

60