Let's analyze Nathan's hypothesis and the provided data.
Nathan hypothesized that as the temperature of liquid water increases, the density decreases because the volume increases. To evaluate this hypothesis, we need to closely examine the relationship between temperature and density in the given data.
Here is the data in a clearer format for reference:
[tex]\[
\begin{array}{|c|c|}
\hline \text{Temperature} \left({ }^{\circ}C\right) & \text{Density} \left(g/cm^3\right) \\
\hline 0.0 & 0.999841 \\
\hline 1.0 & 0.999900 \\
\hline 2.0 & 0.999941 \\
\hline 3.0 & 0.999965 \\
\hline 4.0 & 0.999973 \\
\hline 5.0 & 0.999965 \\
\hline 6.0 & 0.999941 \\
\hline
\end{array}
\][/tex]
First, we observe the trend in the data:
- From [tex]\(0.0^\circ C\)[/tex] to [tex]\(4.0^\circ C\)[/tex], the density increases.
- From [tex]\(4.0^\circ C\)[/tex] to [tex]\(6.0^\circ C\)[/tex], the density decreases.
Nathan's hypothesis is only partially supported by the data. According to his hypothesis, density should continually decrease as temperature increases, which is not entirely true according to the data. While the data shows that density decreases after reaching [tex]\(4.0^\circ C\)[/tex], before [tex]\(4.0^\circ C\)[/tex], the density actually increases as temperature rises.
Based on this analysis, we can consider the appropriate next steps in Nathan's investigation:
- The data do not fully support his hypothesis since the density increases from [tex]\(0^\circ C\)[/tex] to [tex]\(4^\circ C\)[/tex], and then it decreases afterwards.
- Therefore, Nathan should investigate why the density is greatest at [tex]\(4^\circ C\)[/tex].
Thus, the best course of action for Nathan is:
The data do not support his hypothesis, so he should investigate why the density is greatest at [tex]\(4^{\circ} C\)[/tex].
This approach can help uncover the reasons behind the anomaly seen at [tex]\(4^\circ C\)[/tex], providing deeper insight into the behavior of water density changes with temperature.
