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Let's analyze the table of values and determine the type of function that models the dataLet's analyze the table of values and determine the type of function that models the  linear, quadratic, or exponential.

The data points are:

\[
\begin{aligned}
(1, 4) \\
(2, 2) \\
(3, 7) \\
(4, 14) \\
(5, 28) \\
\end{aligned}
\]

### 1. Checking for a linear function:
For a linear function \( y = mx + b \), the rate of change (slope) between consecutive points should be constant. Let's calculate the differences in the \( y \)-values:

- From \( (1, 4) \) to \( (2, 2) \), the change in \( y \) is \( 2 - 4 = -2 \).
- From \( (2, 2) \) to \( (3, 7) \), the change in \( y \) is \( 7 - 2 = 5 \).
- From \( (3, 7) \) to \( (4, 14) \), the change in \( y \) is \( 14 - 7 = 7 \).
- From \( (4, 14) \) to \( (5, 28) \), the change in \( y \) is \( 28 - 14 = 14 \).

Since the differences are not constant, this is **not a linear function**.

### 2. Checking for a quadratic function:
For a quadratic function \( y = ax^2 + bx + c \), the second differences in the \( y \)-values should be constant. Let's compute the first and second differences:

- First differences (as already calculated):
  - \( -2 \), \( 5 \), \( 7 \), \( 14 \)

- Second differences:
  - \( 5 - (-2) = 7 \)
  -

Look at the table of x and y values. Write a linear (y = mx + b), quadratic (y = ax^2), or exponential (y = a(b)^x) function that models the data.

Learn how to analyze a table of values and determine the best function (linear, quadratic, or exponential) to model the data. We provide a detailed step-by-step guide using the given data points.

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