To determine the temperature that the soup must reach within the next four hours to be cooled properly, we should follow the guidelines for safe cooling of food. According to food safety standards, once the soup has been cooled to [tex]$70^{\circ} F$[/tex] (or [tex]$21^{\circ} C$[/tex]) within the first two hours, it must be cooled further to a specific safe temperature within the next four hours.
Based on the given question and the step-by-step solution:
1. The initial temperature of the soup was lowered to [tex]$70^{\circ} F$[/tex] ([tex]$21^{\circ} C$[/tex]) within the first two hours.
2. For the soup to be considered properly cooled following the first cooling phase, it must reach a certain temperature within the next four hours.
The safe cooling temperature to be reached within the next four hours is:
a. [tex]$41^{\circ} F \left(5^{\circ} C \right)$[/tex]
Thus, the soup must be cooled to [tex]$41^{\circ} F \left(5^{\circ} C \right)$[/tex] within the next four hours to be considered properly cooled. So, the correct answer is:
a. [tex]$41^{\circ} F \left(5^{\circ} C \right)$[/tex].
