Which type of function best models the data in each table?...

Which type of function best models the data in each table? Write an equation to model the data.
$\begin{array}{|c|c|}\hline x & {y} \\ \hline 0 & {2} \\ \hline 1 & {1.52} \\ \hline 2 & {1} \\ \hline 3 & {0.49} \\ \hline 4 & {0} \\ \hline\end{array}$

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Key Concepts

Mathematical Modeling with Equations

Mathematical modeling involves using algebraic expressions, such as equations, to represent real-world data and the relationships between variables. In the context of the given table, determining the type of function and constructing the corresponding equation allows us to make predictions and understand the underlying pattern in the data.

Linear Function

A linear function is characterized by a constant rate of change, meaning the difference between successive output values is constant. This type of function is typically expressed in the form y = mx + b, where m represents the slope (the constant rate) and b represents the y-intercept (the value of y when x=0). Linear functions are often used when data points suggest a steady, uniform trend, as is the case when the differences between y-values remain nearly the same for equal increments in x.

Slope (Rate of Change)

The slope of a line is the measure of how much the output value (y) changes for each unit increase in the input value (x). In data modeling, calculating the slope helps determine whether the relationship between variables is constant. A consistent difference between successive data points indicates a linear relationship with a reliable, constant rate of change.

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