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Data points $(x, y)$ are given.(a) Draw a scatter plot of the data points.(b) Make semilog and log-log plots of the data.(c) Is a linear, power, or exponential function appropriate for modeling these data?(d) Find an appropriate model for the data and then graph the model together with a scatter plot of the data.$$\begin{array}{|c|c|c|c|c|c|c|}\hline x & {2} & {4} & {6} & {8} & {10} & {12} \\ \hline y & {0.08} & {0.12} & {0.18} & {0.26} & {0.35} & {0.53} \\ \hline\end{array}$$
$\begin{array}{|c|c|c|c|c|c|c|}\hline x & {0.5} & {1.0} & {1.5} & {2.0} & {2.5} & {3.0} \\ \hline y & {4.10} & {3.71} & {3.39} & {3.2} & {2.78} & {2.53} \\ \hline\end{array}$
(a) See explanation for graph.(b) See explanation for graph.(c) Linear(d) $y=-0.6188571429 x+4.368$
Calculus 1 / AB
Chapter 1
Functions and Sequences
Section 5
Logarithms; Semilog and Log-Log Plots
Functions
Campbell University
University of Michigan - Ann Arbor
Boston College
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As you can see, I've graphed this data in an online graphing calculator. Just show it to you. Okay, we concede that essentially, this looks pretty linear. And the reason why is that? If I were to draw a straight line connecting the points, you conceded that it basically goes through every single point. And it's almost exactly linear. So I would say the overall trend of this graph would be a function that is linear. It's not. Exponential is not longer thinks it's not curved. It's a straight lines that has to be.
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