/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 31 Concern the maximum heart rate (... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 31

Concern the maximum heart rate (MHR). which is the maximum number of times a person's heart can safely beat in one minute. If MHR is in beats per minute and \(a\) is age in years, the formulas used to estimate MHR, are $$For females: \mathrm{MHR}=226-a$$ $$For males: MHR \(=220-a$$ Experiments \)^{22}\( suggest that the female MHR decreases by 12 beats per minute by age \)21,\( and by 19 beats per minute by age \)33 .$ Is this consistent with MHR being approximately linear with age?

Short Answer

Expert verified
Yes, the data is consistent with MHR being approximately linear with age.

Step by step solution

01

Understand the formulas involved

The formulas given to estimate MHR (Maximum Heart Rate) are different for males and females. For females, it is \( ext{MHR} = 226 - a \), where \( a \) is the person's age in years. For males, it is \( ext{MHR} = 220 - a \). We need to use the female formula for this exercise.
02

Determine MHR change at specific ages

According to the problem, we have two key data points for females: at age 21, the MHR decreases by 12 beats per minute, and at age 33, the MHR decreases by 19 beats per minute.
03

Calculate MHR at ages 21 and 33 using the formula

Using the formula \( ext{MHR} = 226 - a \),- At age 21: \( ext{MHR} = 226 - 21 = 205 \)- At age 33: \( ext{MHR} = 226 - 33 = 193 \)
04

Analyze the decrease in MHR over years

From age 21 to 33 (a span of 12 years), the MHR decreases from 205 to 193.- MHR decrease = \( 205 - 193 = 12 \).
05

Understand linearity in change

The problem suggests that the MHR decreases by 12 beats per minute between ages 21 and 33, which is consistent with a decrease of approximately 1 beat per minute each year. This consistent rate implies a linear relationship between age and MHR.
06

Conclusion based on analysis

Since the rate of change (about 1 beat per year) is consistent between the given years, the MHR being approximately linear with age is consistent with the data provided. The formula reflects this linear decrease accurately.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Linear Relationship
A linear relationship in mathematics generally means that two variables are connected in such a way that changes in one variable result in proportional changes in the other. In the context of Maximum Heart Rate (MHR) and age, a linear relationship implies that as age increases, the MHR decreases at a consistent rate. This means for every year increase in age, the MHR drops by about the same amount.

In the exercise you dealt with, you saw that from age 21 to age 33, the MHR decreased consistently by about 1 beat per year. This consistency portrays that the MHR decreases in a linear fashion as a person ages, making it easier to predict MHR at different ages using a simple formula.
Age Factors
Age plays a crucial role in determining the Maximum Heart Rate as evidenced by the equations provided. With increased age, both male and female maximum heart rates tend to decrease. This understanding highlights the age-related decline in cardiovascular capacity, which is a natural part of aging.

In the formulas, age is directly subtracted from a base number (226 for females and 220 for males) to determine the MHR. For instance, in females, as age increases by one year, their MHR reduces by that same amount. This signifies that the determining factor for the decline in MHR is predominantly age, emphasizing its significant impact in cardiovascular health metrics.
Gender Differences
The formula for estimating Maximum Heart Rate differs between males and females. This discrepancy is due to physiological and hormonal differences that can affect heart function.

For females, the base constant is 226, whereas for males, it is 220. This implies that independent of age, females start with a slightly higher potential MHR than males. The difference of 6 beats in the constants indicates the subtle differences in cardiovascular dynamics between genders. Recognizing this difference is crucial for providing accurate health assessments and exercise recommendations.
Formula Analysis
The formula for Maximum Heart Rate is a simple linear equation where age directly affects the result. For females, Maximum Heart Rate is calculated using the formula \( ext{MHR} = 226 - a \), and for males, \( ext{MHR} = 220 - a \).

This straightforward subtraction tells us two important things:
  • The base number (226 for females, 220 for males) represents the theoretical maximum MHR when age is zero.
  • Each unit increase in age reduces the MHR by exactly one beat, demonstrating a clear linear relationship.
By analyzing this formula, we not only see how it reflects physical phenomena but also how it allows for simple computation of expected MHR values at various ages, facilitating easy monitoring of cardiovascular health trends across different ages.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A person breathes in and out every three seconds. The volume of air in the person's lungs varies between a minimum of 2 liters and a maximum of 4 liters. Which of the following is the best formula for the volume of air in the person's lungs as a function of time? (a) \(y=2+2 \sin \left(\frac{\pi}{3} t\right) \quad\) (b) \(\quad y=3+\sin \left(\frac{2 \pi}{3} t\right)\) (c) \(y=2+2 \sin \left(\frac{2 \pi}{3} t\right)\) (d) \(y=3+\sin \left(\frac{\pi}{3} t\right)\)

For Problems \(1-16,\) solve for \(t\) using natural logarithms. $$a=b^{t}$$

Find the present value of an 8000 payment to be made in 5 years. The interest rate is \(4 \%\) per year compounded continuously.

Hydroelectric power is electric power generated by the force of moving water. The table shows the annual percent change in hydroelectric power consumption by the US industrial sector. $$\begin{array}{c|c|c|c|c|c} \hline \text { Year } & 2005 & 2006 & 2007 & 2008 & 2009 \\ \hline \text { \% growth over previous yr } & -1.9 & -10 & -45.4 & 5.1 & 11 \\ \hline \end{array}$$ (a) According to the US Department of Energy, the US industrial sector consumed about 29 trillion BTUs of hydroelectric power in \(2006 .\) Approximately how much hydroelectric power (in trillion BTUs) did the US consume in \(2007 ?\) In \(2005 ?\) (b) Graph the points showing the annual US consumption of hydroelectric power, in trillion BTUs, for the years 2004 to \(2009 .\) Label the scales on the horizontal and vertical axes. (c) According to this data, when did the largest yearly decrease, in trillion BTUs, in the US consumption of hydroelectric power occur? What was this decrease?

Table 1.43 gives values for \(g(t),\) a periodic function. (a) Estimate the period and amplitude for this function. (b) Estimate \(g(34)\) and \(g(60)\). Table 1.43 $$\begin{array}{|c|c|c|c|c|c|c|c|c|}\hline t & 0 & 2 & 4 & 6 & 8 & 10 & 12 & 14 \\\\\hline g(t) & 14 & 19 & 17 & 15 & 13 & 11 & 14 & 19 \\\\\hline t & 16 & 18 & 20 & 22 & 24 & 26 & 28 & \\\\\hline g(t) & 17 & 15 & 13 & 11 & 14 & 19 & 17 \\\\\hline\end{array}$$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.