To determine which values to plot in order to show a linear relationship, let's carefully analyze the provided data. We have three columns: "Day," "Number of birds," and "Log(birds)."
Given the values:
[tex]\[
\begin{array}{|c|c|c|}
\hline
\text{Day} & \text{Number of birds} & \text{Log(birds)} \\
\hline
0 & 3 & 0.477 \\
\hline
1 & 7 & 0.845 \\
\hline
2 & 13 & 1.114 \\
\hline
3 & 25 & 1.398 \\
\hline
4 & 52 & 1.716 \\
\hline
5 & 103 & 2.013 \\
\hline
\end{array}
\][/tex]
When considering how to visualize these data points to observe a linear relationship, the typical approach is to identify the pair of variables that transform the data into a near-linear pattern.
Looking at the data, it's common practice to take the logarithm of a set of values to transform an exponential relationship into a linear one. Therefore, by plotting "Number of birds" against "Log(birds)," we aim for a linear trend.
Here's how you should plot the values:
- On the [tex]\( x \)[/tex]-axis, plot "Number of birds": [tex]\([3, 7, 13, 25, 52, 103]\)[/tex]
- On the [tex]\( y \)[/tex]-axis, plot "Log(birds)": [tex]\([0.477, 0.845, 1.114, 1.398, 1.716, 2.013]\)[/tex]
Therefore, the values to plot to show a linear relationship are:
- Number of birds on the [tex]\( x \)[/tex]-axis
- Log(birds) on the [tex]\( y \)[/tex]-axis.
This arrangement helps to visualize the data in a linear form, confirming that plotting "Number of birds" versus "Log(birds)" is the correct choice.
