[Steps Shown] According to Newton’s law of cooling, if an object at temperature T is immersed in a medium having the constant temperature M , then the rate of


Question: According to Newton’s law of cooling, if an object at temperature T is immersed in a medium having the constant temperature M , then the rate of change of T is proportional to the difference of temperature T M . This gives the differential equation.

\[\frac{dT}{dt}=k\left( M-T \right)\]
  1. Solve the differential equation for T
  2. A thermometer reading 100 o is placed in a medium having a constant temperature 70 o . After 6 minutes, the temperature reads 80 o . What is the temperature after 20 minutes?

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