Answer:
After 2 minutes the temperature of the hot chocolate will be 149.46 degrees Fahrenheit.
Step-by-step explanation:
We are going to use the Newton's law of cooling to solve this exercise. The Newton's law of cooling states that the amount of heat lost by a body is proportional to the difference of temperature between the body and the enviroment. We are going to use the following function :
\(T(t)=T_{0}+(T_{i}-T_{0}).e^{-kt}\)
Where ''T(t)'' is the temperature of the body that depends of the variable ''t'' which is time.
Where \(T_{0}\) is the temperature of the surroundings
In this case \(T_{0}\) is the temperature of the freezer
Where \(T_{i}\) is the initial temperature of the body which is cooling. In this case, \(T_{i}\) is the temperature of the hot chocolate
And where ''k'' is a constant. In this case, \(k=0.12\) is a data of the exercise
If we replace all the values in the equation and replacing \(t=2minutes\)
⇒
\(T(2minutes)=0+(190-0).e^{-(0.12).(2)}\)
\(T(2minutes)=(190).(e^{-0.24})=149.46\)
We find that the temperature of the hot chocolate after 2 minutes is 149.46 degrees Fahrenheit
