Question

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

Complex numbers
ANSWERED
asked 2021-06-22

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

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

Answers (1)

2021-06-23

a) Check the 1st differences of the consecutive y-values. Since they are nearly constant, we can use a linear model.
\(\begin{array}{|c|c|} \hline y & \text{1st differences} \\ \hline 100 & \\ \hline 89.5 & 89.5-100=-10.5 \\ \hline 78.9 & 78.9-89.5=-10.6 \\ \hline 68.4 & 68.4-78.9=-10.5 \\ \hline 57.8 & 57.8-68.4=-10.6 \\ \hline \end{array}\)
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 \(y=100.02-10.55x\)

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