To determine the interval during which the temperature is decreasing, we need to analyze the temperature changes between consecutive hours based on the provided data:
[tex]\[
\begin{array}{|c|c|c|c|c|c|c|c|c|c|}
\hline
\text{Time (hours)} & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\
\hline
\text{Temperature (}^{\circ}\text{F)} & 20.50 & 19.82 & 17.42 & 14.02 & 10.82 & 9.50 & 12.22 & 21.62 & 40.82 \\
\hline
\end{array}
\][/tex]
We will calculate the difference in temperature between each consecutive hour:
1. Difference from hour 0 to hour 1: [tex]\(19.82 - 20.50 = -0.68\)[/tex]
2. Difference from hour 1 to hour 2: [tex]\(17.42 - 19.82 = -2.40\)[/tex]
3. Difference from hour 2 to hour 3: [tex]\(14.02 - 17.42 = -3.40\)[/tex]
4. Difference from hour 3 to hour 4: [tex]\(10.82 - 14.02 = -3.20\)[/tex]
5. Difference from hour 4 to hour 5: [tex]\(9.50 - 10.82 = -1.32\)[/tex]
6. Difference from hour 5 to hour 6: [tex]\(12.22 - 9.50 = +2.72\)[/tex]
7. Difference from hour 6 to hour 7: [tex]\(21.62 - 12.22 = +9.40\)[/tex]
8. Difference from hour 7 to hour 8: [tex]\(40.82 - 21.62 = +19.20\)[/tex]
We observe the following temperature trends:
- Decreasing from hour 0 to hour 5
- Increasing from hour 5 to hour 6
- Increasing from hour 6 to hour 7
- Increasing from hour 7 to hour 8
Thus, the interval where the temperature consistently decreases is from hour 0 to hour 5.
Therefore, the correct answer is:
D. from hour 0 to hour 5
