(a) Would you expect a>0 or a<0? What about b? You would expect a 0 and b o. (b) To fit the values of a and b, consider the following data. A patient with BMI of 15, and who does 50 min of activity each day, has risk index h = 150. A patient with BMI of 30, and who does 30 min of activity each day, has risk index h = 405. Use these data to estimate the values of a and b. Use the data to write a system of linear equations. = 150 = 405 (Use integers or decimals for any numbers in the expressions.) Determine the values of a and b. a=D and b=D (Type integers or decimals.) (c) How accurate is this model likely to be? In other words name some other factors besides physical activity and BMI that could affect h, and should therefore be included in the model. What other factors could affect h? Select all that apply. A. Lifestyle choices B. Dietary habits ]C. External stresses
(a) Would you expect a>0 or a<0? What about b? You would expect a 0 and b o. (b) To fit the values of a and b, consider the following data. A patient with BMI of 15, and who does 50 min of activity each day, has risk index h = 150. A patient with BMI of 30, and who does 30 min of activity each day, has risk index h = 405. Use these data to estimate the values of a and b. Use the data to write a system of linear equations. = 150 = 405 (Use integers or decimals for any numbers in the expressions.) Determine the values of a and b. a=D and b=D (Type integers or decimals.) (c) How accurate is this model likely to be? In other words name some other factors besides physical activity and BMI that could affect h, and should therefore be included in the model. What other factors could affect h? Select all that apply. A. Lifestyle choices B. Dietary habits ]C. External stresses
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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![**Title: Understanding the Relationship Between BMI, Physical Activity, and Heart Disease Risk**
**Introduction**
The likelihood of a person developing heart disease is linked to their Body Mass Index (BMI), which is determined by dividing their body mass by their height. Typically, a high BMI indicates that the person is overweight, and this condition is associated with a higher risk of heart disease. Furthermore, heart disease risk is also influenced by a person's physical activity level.
Suppose a person's BMI is represented by \(x\) and their physical activity (measured in minutes of exercise per day) by \(y\). We define \(h\) as the heart disease risk index, where high values of \(h\) indicate a high risk of heart disease, and low values denote a low risk. The relationship is given by:
\[ h(x, y) = ax + by \]
where \(a\) and \(b\) are constants.
**Section A: Analyzing the Constants**
- **Question**: Would you expect \(a > 0\) or \(a < 0\)? What about \(b\)?
- **Answer**: Based on the relationship, we typically expect:
- \(a > 0\): Since higher BMI is associated with increased heart disease risk.
- \(b < 0\): As more physical activity usually reduces heart disease risk.
**Section B: Calculating Constants Using Data**
To find \(a\) and \(b\), consider the following data:
- Patient 1: BMI is 15, with 50 minutes of activity daily. Risk index \(h = 150\).
- Patient 2: BMI is 30, with 30 minutes of activity daily. Risk index \(h = 405\).
Using these data points, we create a system of linear equations:
\[
\begin{align*}
150 &= 15a + 50b \\
405 &= 30a + 30b
\end{align*}
\]
Determine the values of \(a\) and \(b\):
- Solve these equations to find:
- \(a = 15\)
- \(b = -3\)
**Section C: Evaluating Model Accuracy**
**Question**: How accurate is this model likely to be? Identify additional factors beyond physical activity and BMI that could influence heart disease risk.
**Potential Influential Factors**:
- **Lifestyle choices**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fda71f516-efb8-4c35-a511-98b13aff5a74%2F81a80a79-aa66-4be3-ad5b-15ba54224cc1%2F4mnde0s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Understanding the Relationship Between BMI, Physical Activity, and Heart Disease Risk**
**Introduction**
The likelihood of a person developing heart disease is linked to their Body Mass Index (BMI), which is determined by dividing their body mass by their height. Typically, a high BMI indicates that the person is overweight, and this condition is associated with a higher risk of heart disease. Furthermore, heart disease risk is also influenced by a person's physical activity level.
Suppose a person's BMI is represented by \(x\) and their physical activity (measured in minutes of exercise per day) by \(y\). We define \(h\) as the heart disease risk index, where high values of \(h\) indicate a high risk of heart disease, and low values denote a low risk. The relationship is given by:
\[ h(x, y) = ax + by \]
where \(a\) and \(b\) are constants.
**Section A: Analyzing the Constants**
- **Question**: Would you expect \(a > 0\) or \(a < 0\)? What about \(b\)?
- **Answer**: Based on the relationship, we typically expect:
- \(a > 0\): Since higher BMI is associated with increased heart disease risk.
- \(b < 0\): As more physical activity usually reduces heart disease risk.
**Section B: Calculating Constants Using Data**
To find \(a\) and \(b\), consider the following data:
- Patient 1: BMI is 15, with 50 minutes of activity daily. Risk index \(h = 150\).
- Patient 2: BMI is 30, with 30 minutes of activity daily. Risk index \(h = 405\).
Using these data points, we create a system of linear equations:
\[
\begin{align*}
150 &= 15a + 50b \\
405 &= 30a + 30b
\end{align*}
\]
Determine the values of \(a\) and \(b\):
- Solve these equations to find:
- \(a = 15\)
- \(b = -3\)
**Section C: Evaluating Model Accuracy**
**Question**: How accurate is this model likely to be? Identify additional factors beyond physical activity and BMI that could influence heart disease risk.
**Potential Influential Factors**:
- **Lifestyle choices**
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