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2022 AMC 8 Question 9

AMC8 · 2022 AMC 8

Question 9

A cup of boiling water ($212^\circ$ F) is placed to cool in a room whose temperature remains constant at $68^\circ$ F. Suppose the difference between the water temperature and the room temperature is halved every $5$ minutes. What is the water temperature, in degrees Fahrenheit, after $15$ minutes?
  1. $77$
  2. $86$
  3. $92$
  4. $98$
  5. $104$