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Mathematical Reasoning

A scientist is studying red maple tree growth in a state. She measured the trunk diameters of a sample of trees in the same month every other year. The tables show the data for two of the trees.

\begin{tabular}{|r|c|}
\multicolumn{2}{c}{Tree 1} \\
\hline Year & \begin{tabular}{c}
Trunk \\
Diameter \\
(inches)
\end{tabular} \\
\hline 1 & 18.6 \\
\hline 3 & 19.2 \\
\hline 5 & 19.8 \\
\hline 7 & 20.4 \\
\hline 9 & 21.0 \\
\hline 11 & 21.6 \\
\hline 13 & 22.2 \\
\hline
\end{tabular}

Tree 2
\begin{tabular}{|r|c|}
\hline Year & \begin{tabular}{c}
Trunk \\
Diameter \\
(inches)
\end{tabular} \\
\hline 1 & 11.4 \\
\hline 3 & 12.0 \\
\hline 5 & 12.6 \\
\hline 7 & 13.2 \\
\hline 9 & 13.8 \\
\hline 11 & 14.4 \\
\hline 13 & 15.0 \\
\hline
\end{tabular}

The final year in which she will collect data is year 13. Once her data collection is complete, she will predict future red maple tree growth.

Consider the data for year 3 and year 11. What are the locations of the two points on the coordinate grid?

Click on the grid to plot the points.
(Note: To remove a point, place the arrow over the point and click the left mouse button.)



Answer :

GinnyAnswer
To determine the specific points on the coordinate grid for Tree 1 and Tree 2 at years 3 and 11, we need to review the given data and identify the trunk diameters at those particular years for each tree.

The data for Tree 1 and Tree 2 are as follows:

Tree 1:
[tex]\[ \begin{array}{|r|c|} \hline \text{Year} & \text{Trunk Diameter (inches)} \\ \hline 1 & 18.6 \\ \hline 3 & 19.2 \\ \hline 5 & 19.8 \\ \hline 7 & 20.4 \\ \hline 9 & 21.0 \\ \hline 11 & 21.6 \\ \hline 13 & 22.2 \\ \hline \end{array} \][/tex]

Tree 2:
[tex]\[ \begin{array}{|r|c|} \hline \text{Year} & \text{Trunk Diameter (inches)} \\ \hline 1 & 11.4 \\ \hline 3 & 12.0 \\ \hline 5 & 12.6 \\ \hline 7 & 13.2 \\ \hline 9 & 13.8 \\ \hline 11 & 14.4 \\ \hline 13 & 15.0 \\ \hline \end{array} \][/tex]

We are interested in the following data points:
1. For Tree 1 at year 3 and year 11.
2. For Tree 2 at year 3 and year 11.

Let's locate these points one by one.

For Tree 1:
- At year 3:
- Year = 3
- Trunk diameter = 19.2 inches

Thus, the point is [tex]\((3, 19.2)\)[/tex].

- At year 11:
- Year = 11
- Trunk diameter = 21.6 inches

Thus, the point is [tex]\((11, 21.6)\)[/tex].

For Tree 2:
- At year 3:
- Year = 3
- Trunk diameter = 12.0 inches

Thus, the point is [tex]\((3, 12.0)\)[/tex].

- At year 11:
- Year = 11
- Trunk diameter = 14.4 inches

Thus, the point is [tex]\((11, 14.4)\)[/tex].

To summarize, the points for Tree 1 and Tree 2 are:
- Tree 1 at year 3: [tex]\((3, 19.2)\)[/tex]
- Tree 1 at year 11: [tex]\((11, 21.6)\)[/tex]
- Tree 2 at year 3: [tex]\((3, 12.0)\)[/tex]
- Tree 2 at year 11: [tex]\((11, 14.4)\)[/tex]

These are the specific coordinates you should plot on the grid for each respective tree and year.

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