Let's analyze the problem step by step.
Nathan's hypothesis suggests that as the temperature of liquid water increases, its density should decrease because the volume of water should increase with temperature.
Here is the data provided:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Temperature} \; (^{\circ}C) & \text{Density} \; (g/cm^3) \\
\hline
0.0 & 0.999841 \\
1.0 & 0.999900 \\
2.0 & 0.999941 \\
3.0 & 0.999965 \\
4.0 & 0.999973 \\
5.0 & 0.999965 \\
6.0 & 0.999941 \\
\hline
\end{array}
\][/tex]
1. Define Nathan's hypothesis more precisely: According to Nathan, if the temperature goes up, the density should go down.
2. Examine the data trend:
- From 0.0°C to 1.0°C: Density increases.
- From 1.0°C to 2.0°C: Density increases.
- From 2.0°C to 3.0°C: Density increases.
- From 3.0°C to 4.0°C: Density increases slightly.
- From 4.0°C to 5.0°C: Density decreases a bit.
- From 5.0°C to 6.0°C: Density decreases more.
3. Check the consistency with the hypothesis: Nathan's hypothesis suggests a consistent decrease in density with the increase in temperature, but the data shows an initial increase in density until 4.0°C, followed by a decrease afterward.
Therefore, the data does not support Nathan's hypothesis because the density increases up to 4°C and then starts to decrease.
Given this discrepancy:
3. Investigate further:
- One reasonable investigation led by this analysis would be understanding why the density reaches its maximum at 4°C. This is a known physical property of water where its density is highest at 4°C.
Thus, the correct course of action for Nathan, given this data, would be to:
"The data do not support his hypothesis, so he should investigate why the density is greatest at [tex]$4^{\circ} C$[/tex]."
Therefore the correct answer is: Nathan should investigate why the density is greatest at [tex]\(4^{\circ}C\)[/tex].
