# Determine whether a linear, quadratic, or exponential function best models the data. Then, use regression to find the function that models the data. x

Determine whether a linear, quadratic, or exponential function best models the data. Then, use regression to find the function that models the data.

$\begin{array}{|cccccc|}\hline x& 0& 1& 2& 3& 4\\ y& 100& 89.5& 78.9& 68.4& 57.8\\ \hline\end{array}$

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a) Check the 1st differences of the consecutive y-values. Since they are nearly constant, we can use a linear model.
$\begin{array}{|cc|}\hline y& \text{1st differences}\\ 100& \\ 89.5& 89.5-100=-10.5\\ 78.9& 78.9-89.5=-10.6\\ 68.4& 68.4-78.9=-10.5\\ 57.8& 57.8-68.4=-10.6\\ \hline\end{array}$
b)At the WolframAlpha web site you can enter: fit linear $\left\{\left\{0,100\right\},\left\{1,89.5\right\},\left\{2,78.9\right\},\left\{3,68.4\right\},\left\{4,57.8\right\}\right\}$
Which results i $y=100.02-10.55x$