Question

Following a law suit when a woman was burned by spilling hot coffee, McDonalds now serves coffee at 155°F. The room temperature at McDonalds is 70°F. According to Newtons Law of Cooling, the rate of change of the temperature of hourly coffee is proportional to the difference between the temperature of the coffee and the surrounding room temperature. In this situation, we have the model

Model and the rest of the question is in the picture.

Answer 1

Given that the temperature of tea was modeled by :
T(t)=110e^(-0.019t)+T
the temperature of the coffee when t=0 will be:
T(0)=110e^(-0.019*0)+70
T(0)=110+70=180° F

b] Time taken for the temperature to cool to 155° F will be:
155=110e^(-0.019t)+70
85=110e^(-0.019t)
solving for t we get:
t=13.57 minutes