https://file.aiquickdraw.com/mathbot/file/1726174451468b0x3vr3r.jpg

Let's analyze the table from the image. The provided data consists of the following pairs:

| x | y  |
|---|----|
| 1 | 7  |
| 2 | 7/2 |
| 3 | 7  |
| 4 | 14 |
| 5 | 28 |

We need to find if the data follows a **linear** ( \( y = mx + b \) ), **quadratic** ( \( y = ax^2 \) ), or **exponential** ( \( y = ab^x \) ) model.

Let’s examine the pattern:

### 1. Linear Model:
In a linear relationship, the difference in \( y \)-values between consecutive \( x \)-values should be constant. Let's calculate the differences:
- Between \( x=1 \) and \( x=2 \): \( 7 - \frac{7}{2} = \frac{7}{2} \)
- Between \( x=2 \) and \( x=3 \): \( \frac{7}{2} - 7 = -\frac{7}{2} \)
- Between \( x=3 \) and \( x=4 \): \( 7 - 14 = -7 \)
- Between \( x=4 \) and \( x=5 \): \( 14 - 28 = -14 \)

Since the differences are not constant, the data is **not linear**.

### 2. Quadratic Model:
In a quadratic model, the second differences (the difference of the differences) should be constant. Let's calculate the second differences:
-

Write a linear, quadratic, or exponential function that models the data from the table: x = [1, 2, 3, 4, 5] and y = [7, 7/2, 7, 14, 28].

Learn how to determine if a dataset fits a linear, quadratic, or exponential model. Analyze the provided x and y values, explore differences and patterns, and find the appropriate mathematical function to model the data. Suitable for Algebra students in Grades 9-10.

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