Question

50 POINTSSS

Answer 1

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}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}T

0

is the temperature of the surroundings

In this case T_{0}T

0

is the temperature of the freezer

Where T_{i}T

i

is the initial temperature of the body which is cooling. In this case, T_{i}T

i

is the temperature of the hot chocolate

And where ''k'' is a constant. In this case, k=0.12k=0.12 is a data of the exercise

If we replace all the values in the equation and replacing t=2minutest=2minutes

⇒

T(2minutes)=0+(190-0).e^{-(0.12).(2)}T(2minutes)=0+(190−0).e

−(0.12).(2)

T(2minutes)=(190).(e^{-0.24})=149.46T(2minutes)=(190).(e

−0.24

)=149.46

We find that the temperature of the hot chocolate after 2 minutes is 149.46 degrees Fahrenheit