Suppose that Tammy's blood pressure can be modeled by the following function. p (t) = 91 +24 cos (89 nt)
Suppose that Tammy's blood pressure can be modeled by the following function. p (t) = 91 +24 cos (89 nt)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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## Modeling Blood Pressure with a Mathematical Function
### Mathematical Model of Tammy's Blood Pressure
Suppose that Tammy's blood pressure can be modeled by the following function:
\[ p(t) = 91 + 24 \cos (89\pi t) \]
Tammy's blood pressure increases each time her heart beats, and it decreases as her heart rests in between beats. In this equation, \( p(t) \) is the blood pressure in mmHg (millimeters of mercury), and \( t \) is the time in minutes.
### Objectives
Find the following. If necessary, round to the nearest hundredth:
- Amplitude of \( p \): \_\_\_ mmHg
- Number of heartbeats per minute: \_\_\_
- Period of \( p \): \_\_\_ minutes
### Explanation
**Amplitude of \( p \)**: This represents the maximum deviation from the average blood pressure value. It indicates how much Tammy's blood pressure fluctuates.
**Number of Heartbeats Per Minute**: This is derived from the frequency of the cosine function in the model.
**Period of \( p \)**: This is the time it takes for Tammy's blood pressure to complete one full cycle of increase and decrease.
### Diagram/Interactive Element
- A dialog box for inputting the amplitude, number of heartbeats per minute, and period.
- Buttons labeled "Check," "Save For Later," and "Submit Assignment."
---
Make sure the values you input are rounded to the nearest hundredth if necessary.
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## Modeling Blood Pressure with a Mathematical Function
### Mathematical Model of Tammy's Blood Pressure
Suppose that Tammy's blood pressure can be modeled by the following function:
\[ p(t) = 91 + 24 \cos (89\pi t) \]
Tammy's blood pressure increases each time her heart beats, and it decreases as her heart rests in between beats. In this equation, \( p(t) \) is the blood pressure in mmHg (millimeters of mercury), and \( t \) is the time in minutes.
### Objectives
Find the following. If necessary, round to the nearest hundredth:
- Amplitude of \( p \): \_\_\_ mmHg
- Number of heartbeats per minute: \_\_\_
- Period of \( p \): \_\_\_ minutes
### Explanation
**Amplitude of \( p \)**: This represents the maximum deviation from the average blood pressure value. It indicates how much Tammy's blood pressure fluctuates.
**Number of Heartbeats Per Minute**: This is derived from the frequency of the cosine function in the model.
**Period of \( p \)**: This is the time it takes for Tammy's blood pressure to complete one full cycle of increase and decrease.
### Diagram/Interactive Element
- A dialog box for inputting the amplitude, number of heartbeats per minute, and period.
- Buttons labeled "Check," "Save For Later," and "Submit Assignment."
---
Make sure the values you input are rounded to the nearest hundredth if necessary.
---
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