50 POINTSSS Suppose you make coffee and it starts off just too hot to drink, so you put it in the refrigerator temporarily to cool it off. If the original temperature is 190 degrees Fahrenheit and the refrigerator is 36 degrees Fahrenheit, what will the temperature of the coffee be after 3 minutes? (k = 0.12)

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

Yea what she said ^^^

Step-by-step explanation:

equal to

step-by-step explanation: