Question

Suppose you make hot chocolate. It's too hot to drink, so you put it in the freezer to cool it off. If the original temperature is 190 degrees Fahrenheit and the freezer is 0 degrees Fahrenheit, what will the temperature of the hot chocolate be after 3 minutes? (k = 0.12)

272.33 degrees

132.56 degrees

241.54 degrees

149.46 degrees

Answer 1

Answer:

Option 2.

Step-by-step explanation:

Given information: k=0.12, initial temperature = 190 degrees Fahrenheit and the freezer temperature = 0 degrees Fahrenheit

Newton's Law of cooling

$T(t)=T_1+(T_0-T_1)e^{-kt}$

where,  

T(t) is temperature a time t.

$T_1$ is temperature of surrounding environment.

$T_0$ is initial temperature of object.

k is constant (Different for each object)

Substitute $T_1=0, T_0=190$ and k=0.12 in the above equation.

$T(t)=0+(190-0)e^{-0.12t}$

$T(t)=190e^{-0.12t}$

We need to find the temperature of the hot chocolate after 3 minutes.

Substitute t=3 in the above equation.

$T(3)=190e^{-0.12(3)}$

$T(3)=132.558501953$

$T(3)\approx 132.56$

Therefore, the correct option is 2.