Question

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)

Answer 1

im confuse

Answer 2

@darkknight

Answer 3

For this question we will use Newton's Law of Cooling to derive the answer.

The function is:
\[T(t)=Tₒ+(Tᵢ-Tₒ) *e^(kt)\]

T = Tempature
t = Time
Tₒ - Tempature of Surroundings
Tᵢ - Intial Tempature
k - Our constant that's been given

We have all our values in the question above, it's just time to plug them in.

\[T(3) = 36+(190+36)*e^(-0.36)\]

Solving through we get our final answer:

\[T(3)=143.4\]

Meaning after 3 minutes in a 36 Fahrenheit fridge, the coffee cools down to 143.4 degrees Fahrenheit

Answer 4

I dunno why the exponents were being super weird, but basically (-kt) is the exponent of (e). With that you can also infer that (-0.36) is also an exponent of (e) in the second step. Just wanted to make that clear incase you got confused

Answer 5

try ur best bro