To find the change in temperature from 9 a.m. to noon, we need to subtract the temperature at 9 a.m. from the temperature at noon.
Let \( T_{9am} = -5.8^\circ C \) (temperature at 9 a.m.)
Let \( T_{noon} = -1.6^\circ C \) (temperature at noon)
The change in temperature (\( \Delta T \)) can be calculated using the following equation:
\[ \Delta T = T_{noon} - T_{9am} \]
Substituting the values:
\[ \Delta T = -1.6 - (-5.8) \]
This simplifies to:
\[ \Delta T = -1.6 + 5.8 \]
Now performing the addition:
\[ \Delta T = 4.2 \]
So, the change in temperature during these three hours is \( 4.2^\circ C \).
Explanation of the Answer
The positive result of \( 4.2^\circ C \) indicates that the temperature increased. Specifically, the air temperature rose from \( -5.8^\circ C \) at 9 a.m. to \( -1.6^\circ C \) at noon. This change signifies a warming trend in the temperature over the three-hour period.