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

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

$$\begin{array}{|c|c|} \hline x&0&1&2&3&4\\ \hline y&10089&578&968&457&8\\ \hline \end{array}$$

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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.
y | 1st differences
$$100 |$$
$$89.5 | 89.5-100=-10.5$$
$$78.9 | 78.9-89.5=-10.6$$
$$68.4 | 68.4-78.9=-10.5$$
$$57.8 | 57.8-68.4=-10.6$$
b)At the WolframAlpha web site you can enter: fit linear $${{0,100},{1,89.5},{2,78.9},{3,68.4},{4,57.8}}$$
Which results i $$y=100.02-10.55x$$