The table gives the percent of total households that have married couples for selected years from 1982 and projected to 2050. Complete parts (a) through (c) below. OA. y=(x²+x+ (Type integers or decimals rounded to three decimal places as needed.) b. Graph the function and the data points on the same axes. Choose the correct graph below. Fur a. Find the quadratic function that best models the data, with x representing the number of years after 1980 and y representing the percent. O B. *** بما Q Year Percent 1982 59 1990 56 2000 54 2010 49 O C. Q Q Year 2020 2030 2040 2050 OD. Percent 47 46 45 44 Q Q
The table gives the percent of total households that have married couples for selected years from 1982 and projected to 2050. Complete parts (a) through (c) below. OA. y=(x²+x+ (Type integers or decimals rounded to three decimal places as needed.) b. Graph the function and the data points on the same axes. Choose the correct graph below. Fur a. Find the quadratic function that best models the data, with x representing the number of years after 1980 and y representing the percent. O B. *** بما Q Year Percent 1982 59 1990 56 2000 54 2010 49 O C. Q Q Year 2020 2030 2040 2050 OD. Percent 47 46 45 44 Q Q
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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![### Educational Website Content: Analyzing Household Data Over Time
**Table Overview:**
The table presents the percentage of total households with married couples for selected years from 1982, with projections up to 2050.
| Year | Percent | Year | Percent |
|------|---------|------|---------|
| 1982 | 59 | 2020 | 47 |
| 1990 | 56 | 2030 | 46 |
| 2000 | 54 | 2040 | 45 |
| 2010 | 49 | 2050 | 44 |
**Quadratic Function Modeling:**
a. The exercise requires finding the quadratic function \( y = ax^2 + bx + c \) that best models the data. Here, \( x \) represents the number of years after 1980, and \( y \) represents the percent of households.
- **Equation Form:** \( y = [\ \ ]x^2 + [\ \ ]x + [\ \ ] \)
- You are instructed to type integers or decimals rounded to three decimal places as needed.
**Graph Analysis:**
b. The task involves graphing the quadratic function along with the data points and selecting the correct graph from the options A, B, C, or D.
- **Graph Options:**
- **A:** Displays a curve with data points trending downwards.
- **B:** Displays a curve with steeper downward trend.
- **C:** Displays a curve with data points showing a gentle decline.
- **D:** Displays a curve with data points showing a less steep decline.
Students must identify which graph correctly represents both the curve of the quadratic function and the data points from the table.
**Interactive Component:**
After analyzing and choosing the correct graph, students can proceed by clicking the 'Next' button to continue to the subsequent part of the lesson.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F556745e6-02d3-4800-a933-7dc40a753d9d%2Fd47e4b47-f4a7-4271-8b16-635d22a5c65e%2Fb02wkf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Educational Website Content: Analyzing Household Data Over Time
**Table Overview:**
The table presents the percentage of total households with married couples for selected years from 1982, with projections up to 2050.
| Year | Percent | Year | Percent |
|------|---------|------|---------|
| 1982 | 59 | 2020 | 47 |
| 1990 | 56 | 2030 | 46 |
| 2000 | 54 | 2040 | 45 |
| 2010 | 49 | 2050 | 44 |
**Quadratic Function Modeling:**
a. The exercise requires finding the quadratic function \( y = ax^2 + bx + c \) that best models the data. Here, \( x \) represents the number of years after 1980, and \( y \) represents the percent of households.
- **Equation Form:** \( y = [\ \ ]x^2 + [\ \ ]x + [\ \ ] \)
- You are instructed to type integers or decimals rounded to three decimal places as needed.
**Graph Analysis:**
b. The task involves graphing the quadratic function along with the data points and selecting the correct graph from the options A, B, C, or D.
- **Graph Options:**
- **A:** Displays a curve with data points trending downwards.
- **B:** Displays a curve with steeper downward trend.
- **C:** Displays a curve with data points showing a gentle decline.
- **D:** Displays a curve with data points showing a less steep decline.
Students must identify which graph correctly represents both the curve of the quadratic function and the data points from the table.
**Interactive Component:**
After analyzing and choosing the correct graph, students can proceed by clicking the 'Next' button to continue to the subsequent part of the lesson.
Transcribed Image Text:**Comment on the fit. Choose the correct answer below.**
- **A.** The model is a poor fit because it does not pass close to any of the data points.
- **B.** The model is a good fit because it passes close to all of the data points.
- **C.** The model is a mediocre fit because it passes close to some of the data points.
- **D.** The model is an excellent fit because it passes through all of the data points.
**c. Use the model to find the predicted percent of total households that have married couples in 2033.**
The predicted percent of total households that have married couples in 2033 is approximately ____%. (Round to the nearest whole number as needed.)
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