Precalculus: Mathematics for Calculus - 6th Edition
6th Edition
ISBN: 9780840068071
Author: Stewart, James, Redlin, Lothar, Watson, Saleem
Publisher: Cengage Learning
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Textbook Question
Chapter 5.6, Problem 29E
Blood Pressure Each time your heart beats, your blood pressure increases, then decreases as the heart rests between beats. A certain person’s blood pressure is modeled by the function
where p(t) is the pressure (in mmHg) at time t, measured in minutes.
- (a) Find the amplitude, period, and frequency of p.
- (b) Sketch a graph of p.
- (c) If a person is exercising, his or her heart beats faster. How does this affect the period and frequency of p?
(a)
Expert Solution
To determine
The value of amplitude, period and frequency of p for the given function.
Answer to Problem 29E
The value of amplitude for the equation
Explanation of Solution
Given:
The function which gives the blood pressure of a certain person at time t in minutes is
Calculation:
The general form of the sine function representing harmonic motion is shown below.
Where,
a is amplitude.
b is the average oscillation of an object.
c represents the position of an object at
The given function is shown below.
Compare the equation (1) and equation (2), then the value of a is 25, the value of
The formula to obtain time period p taken by an object to complete one cycle is shown below.
Substitute
Reciprocate the time period to find the value of frequency as shown below,
Substitute
Therefore, the value of amplitude is 25, the value of time period is
(b)
Expert Solution
To determine
To sketch: The graph for the given function.
Explanation of Solution
The given function is shown below.
The representation of the function
Figure (1)
Therefore, the graph of the function
(c)
Expert Solution
To determine
The effect on period and frequency when the heart of a man beats faster while exercising.
Explanation of Solution
A person’s heart beat increases while exercising implies that the frequency is increasing.
Time period is reciprocal of frequency therefore, whenever frequency increases time period decreases.
Thus, the frequency increases and time period decreases as a person exercises.
Chapter 5 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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