Example: Each time your heart beats, your blood pressure increases, then decreases as the heart rests between beats. A particular individual has blood pressure which has been modeled with the function:
\[ BP(t) = 103+17\cos(120\pi t) \]where \(BP\) is pressure measured in mmHg and \(t\) is time in minutes.
- What is the amplitude, period, and frequency of the blood pressure?
- Systolic blood pressure refers to the peak blood pressure, which happens when the heart contracts, whereas diastolic pressure is when the heart fully expands, and the blood pressure is the lowest. What is this individual's systolic and diastolic values?
- Sketch a graph of \(BP(t)\) with at least two periods.
- What is this individual's heart rate?
Solution
- Amplitude: 17, Period: \(\frac{2\pi}{120\pi}=\frac{{1}}{{60}}\), Frequency: \(\frac{{1}}{{P}} = 60\)
- 120/86
- See sketch below
- The person's heart rate can be measured as the distance between peaks (contractions of the heart) which is the the period: 1 beat every 1/60 minutes, e.g., 1 beat per second or 60 beats per minute.