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MATHEMATICS - CASE STUDY

    Introduction



Hot Cereal
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Ms. Jamison overheated her cereal in the morning and needs to wait while it cools before she cant eat it. If the cooling rate is known, she wonders how she might calculate the waiting time.

What is known:

  • The cereal was heated to 90°C.
  • After 1 minute, the cereal cooled to 60°C.
  • the room temperature is 25°C.
  • Ms. Jamison starts her breakfast when the cereal's temperature is 40°C.
  • The temperature difference between the cereal and the room changes with time according to the following equation
         dθ/dt = kθ
    where θ is the temperature difference of the cereal and room; t is the time and k is the cooling constant.
     
    Questions

 

 

How long does it take for the cereal to cool so that Ms. Jamison can start her breakfast?

     
    Approach


 

Since the cooling rate of the temperature is proportional to its current temperature, this problem can be considered as an exponential decay problem.