Final answer:
Use a Class K fire extinguisher for kitchen grease fires, as it emits a mist and fluorinated foam formulated to put out fires involving cooking oils, fats, and greases.
Step-by-step explanation:
For a kitchen grease fire in a homeless shelter, the appropriate type of fire extinguisher to use is a Class K extinguisher. These are specifically designed to handle fires involving cooking oils, fats, and grease that can occur in kitchens. They work by releasing a fine mist that helps cool the fire and a fluorinated solution which spreads across the burning surface to effectively extinguish the fire. The fluorinated foam is now universally used to fight large-scale fires of organic liquids, making these extinguishers very effective for kitchen fires. It is important to note that dry-cleaning solvents were once used in fire extinguisher systems and for fighting fires, but these are no longer recommended due to safety concerns.