Presenting data in the form of table. For the data set shown by the table.Create a scatter plot for the data.Use the scatter plot to determine whether an exponential function, a logarithmic function, or a linear function is the best choice for modeling the data.

UkusakazaL 2021-08-08

Presenting data in the form of table. For the data set shown by the table, Solve,
a) Create a scatter plot for the data.
b) Use the scatter plot to determine whether an exponential function, a logarithmic function, or a linear function is the best choice for modeling the data. (If applicable, you will use your graphing utility to obtain these functions.)
\(\begin{array}{|c|c|}\hline \text{Intensity (wattd per}\ meter^{2}) & \text{Loudness Level (decibels)} \\ \hline 0.1\text{(loud thunder)} & 110 \\ \hline 1\text{(rock concert, 2 yd from speakers)} & 120 \\ \hline 10 \text{(jackhammer)} & 130 \\ \hline 100 \text{(jet take off, 40 yd away)} & 140 \\ \hline \end{array}\)

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Answered 2021-08-16 Author has 28097 answers

Step 1
a) We can draw scatter plot using Excel as follows,
Enter the data in Excel and select it.
Go to insert \(\displaystyle\rightarrow\) scatter \(\displaystyle\rightarrow\) select 1st scatter plot \(\displaystyle\rightarrow\) add trendline to the plot \(\displaystyle\rightarrow\) Tick on display equation on plot and display R square on the plot.
We get result as follows,
image
Step 2
b) From the above scatter plot, we can observe that, the regression equation for logarithmic model is,
\(\displaystyle\hat{{{y}}}={4.3429}{\ln{{\left({x}\right)}}}+{120}\)
and \(\displaystyle{R}^{{{2}}}={1}\)
Since, the value of \(\displaystyle{R}^{{{2}}}={1}\) for Logarithmic function, the logarithmic function is the best choice for modeling the data.

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