One of the two tables below shows data that can best be modeled by a linear function, and the other shows data that can best be modeled by a quadratic function. Identify which table shows the linear data and which table shows the quadratic data, and find formula for each model. linear function Table A x 0 f(x) 9 Table B X 0 1 g(x) 9 16 (f(x) 16 --Select-- quadratic function ✓ f(x) g(x) 27 42 61 3 4 2 23 30 37
One of the two tables below shows data that can best be modeled by a linear function, and the other shows data that can best be modeled by a quadratic function. Identify which table shows the linear data and which table shows the quadratic data, and find formula for each model. linear function Table A x 0 f(x) 9 Table B X 0 1 g(x) 9 16 (f(x) 16 --Select-- quadratic function ✓ f(x) g(x) 27 42 61 3 4 2 23 30 37
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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Transcribed Image Text:### Identifying Data Models: Linear vs. Quadratic Functions
#### Introduction
One of the two tables below shows data that can best be modeled by a linear function, and the other shows data that can best be modeled by a quadratic function. Identify which table shows the linear data and which table shows the quadratic data, and find a formula for each model.
#### Table A
| x | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| f(x) | 9 | 16 | 27 | 42 | 61 |
#### Table B
| x | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| g(x) | 9 | 16 | 23 | 30 | 37 |
#### Linear Function Analysis
You can use the drop-down menu to select which function (f(x) or g(x)) corresponds to the linear function. Based on the examination of the data in Table A and Table B, it appears that the values in Table B increase by a constant amount (linear behavior), whereas the values in Table A do not increase by a constant amount (indicative of quadratic behavior).
| x | 0 | 1 | 2 | 3 | 4 |
|----|----|----|----|----|----|
| g(x)| 9 | 16 | 23 | 30 | 37 |
#### Quadratic Function Analysis
The values in Table A can be shown to follow a quadratic pattern. The differences between consecutive terms show a second difference that is constant, indicating a quadratic function.
| x | 0 | 1 | 2 | 3 | 4 |
|-----|----|----|----|----|----|
| f(x)| 9 | 16 | 27 | 42 | 61 |
#### Conclusion
By analyzing the tables, you can identify:
- Table A displays the quadratic data.
- Table B displays the linear data.
Select the function using the drop-down menu accordingly and input the formulas for each model.
Make sure to verify your calculations or use technology to assist in finding the exact formulas.
### Interactive Components
- **Drop-down Menu**: Use the provided drop-down menu to select `f(x)`
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