2022 AMC 8
Complete problem set with solutions and individual problem pages
A cup of boiling water () is placed to cool in a room whose temperature remains constant at . Suppose the difference between the water temperature and the room temperature is halved every minutes. What is the water temperature, in degrees Fahrenheit, after minutes?
- A.
- B.
- C.
- D.
- E.
Initially, the difference between the water temperature and the room temperature is degrees Fahrenheit.
After minutes, the difference between the temperatures is degrees Fahrenheit.
After minutes, the difference between the temperatures is degrees Fahrenheit.
After minutes, the difference between the temperatures is degrees Fahrenheit. At this point, the water temperature is degrees Fahrenheit.
Remark:
Alternatively, we can condense the solution above into the following equation:
