(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 191Â°F is poured into a cup to brew tea. After steeping for 3 minutes, the tea has a temperature of 166Â°F. The temperature of the room is 79Â°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)=Â Â Â Â

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

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

It will take ______________ minutes.

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This question was answered on: Sep 05, 2019

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