Example 7 from Precalculus, 7.6 Modeling with Trigonometric Functions

Interpreting the Periodic Behavior Equation

The average person’s blood pressure is modeled by the function $f (t) = 20 \sin (160 π t) + 100,$ where $f (t)$ represents the blood pressure at time $t,$ measured in minutes. Interpret the function in terms of period and frequency. Sketch the graph and find the blood pressure reading.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
The period is given by

$\begin{array}{l} \begin{array}{l} \frac{2 π}{ω} = \frac{2 π}{160 π} \\ = \frac{1}{80} \end{array} \end{array}$
In a blood pressure function, frequency represents the number of heart beats per minute. Frequency is the reciprocal of period and is given by

$\begin{matrix} \frac{ω}{2 π} = \frac{160 π}{2 π} \\ = 80 \end{matrix}$

See the graph in Figure 11.

Figure 11 The blood pressure reading on the graph is $\frac{120}{80} (\frac{maximum}{minimum}) .$

How did it go?

Solution

Solution