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(Solved) Hot water at a temperature of 191F is poured into a cup to brew tea. After steeping for 3 minutes, the tea has a temperature of 166F. The temperature...


Hot water at a temperature of 191°F is poured into a cup to brew tea. After steeping for 3 minutes, the tea has a temperature of 166°F. The temperature of the room is 79°F.

(a) Write a differential equation modeling the change in temperature (in degrees Fahrenheit) with respect to time (in minutes). If necessary, use T for temperature and t for time, and k for any undetermined constants.

dT/dt=

(b) Find an equation for the temperature TT of the tea in degrees Fahrenheit as a function of time t in minutes.

T(t)=    

(c) What will the temperature of the tea be 30 minutes after it was poured? After 30 minutes, the temperature will be ________ °F.

(d) How many minutes after the water was poured will the tea have cooled to a temperature of 150°F?

It will take ______________ minutes.

 


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