Chapter 13.8, Problem 13CYU

To determine

Find the function that represents the person’s blood pressure P at time t seconds. Also draw the graph.

Answer to Problem 13CYU

The sine function for the person’s blood pressure is $y=20\sin 180\pi \theta +110$ .

Explanation of Solution

Given: It is given in the question that a person’s blood pressure oscillates between a maximum of $130$ and a minimum of $90$ . The person’s heart rate is $90$ beats per minutes.

Concept Used:

In this, use the concept of the general equation for sine $y=a\sin b\theta +d$ , where a is amplitude , $\frac{2\pi }{\left|b\right|}$ is period and d is the vertical shift .

Calculation: Let the function be $y=a\sin b\theta +d$ .

Here, The maximum is $130$ and the minimum is $90$ .

Average of the above = $\frac{130+90}{2}=\frac{220}{2}=110$ which is the vertical shift (because the average of max and min).

Since, frequency is $90$ beats per minute, so the period is $\frac{1}{90}$ , so $\frac{2\pi }{\left|b\right|}=\frac{1}{90}\Rightarrow b=180\pi$ .

And the amplitude is the distance from the midline to the max/ min, so $a=20$ .

Hence ,the function is $y=20\sin 180\pi \theta +110$ .

The graph of the function is given below:

  

Conclusion:

The function is $y=20\sin 180\pi \theta +110$ .