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

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: