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As the heart beats, blood pressure increases and decreases. This happens cyclically at the rate of the person’s heart beat. A doctor is monitoring the blood pressure of a patient whose heart rate is 70 beats per minute. The maximum blood pressure over the course of a 10-minute period is 120 mm/Hg and the minimum is 60 mm/Hg. Find a sine function that models the person’s blood pressure as a function of time (in minutes). F(x) = 30 sin(140πt) 90 f(x) = 60 sin(70πt) 30 f(x) = 60 sin(140πt) 90 f(x) = 30 sin(70πt) -60.

Respuesta :

Sin function goes up and down, standard amplitude is 1 unit. The sin function modelling the given situation is [tex]f(x) = 30\sin(\dfrac{\pi x}{5}) + 90[/tex]

How does sine function works?

Suppose that we've got

[tex]f(x) = a\sin(bx + c) + d[/tex]

It has got

  • Amplitude or maximum height from average motion horizontal axis = a+d
  • And thus, the minimum low from horizontal axis is -a (sin ranges from -1 to 1, and multiplying a to it make it range from -a + d to a).
  • Period of wave: [tex]\dfrac{2\pi}{b}[/tex]
  • Phase shift (horizontal left shift) = c/b
  • Horizontal line around which wave moves is: y = d

The situation given has:

Maximum blood pressure as 120 mm/Hg = a + d

Minimum blood pressure as 60 mm/Hg = -a + d

Thus, adding both will give:

[tex](a+d) + (-a + d) = 120 + 60\\2d = 180\\d = 90[/tex]

Thus, as a + d = 120, thus, a = 120-d = 120 - 90 = 30

Now, The period is given to  be 10 minutes, or we get:

[tex]\dfrac{2\pi}{b} = 10\\\\b = \dfrac{\pi}{5}[/tex]

Since count started from 0, thus, c= 0

Therefore, the sine function modelling the given situation is:

[tex]f(x) = a\sin(bx + c) + d \\\\f(x) = 30\sin(\dfrac{\pi x}{5}) + 90[/tex]

Here x is the number of minutes passed.

Learn more about sine function modelling the situation here:

https://brainly.com/question/12070030

Answer:

A

Step-by-step explanation:

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