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This problem can be solved using **Newton's Law of Cooling**, which states:

\[
T(t) = T_{\text{room}} + (T_0 - T_{\text{room}}) e^{-kt}
\]

Where:
- \( T(t) \) is the temperature at time \( t \),
- \( T_{\text{room}} \) is the ambient (room) temperature,
- \( T_0 \) is the initial temperature of the object (the coffee),
- \( k \) is a constant related to the rate of cooling,
- \( t \) is the time that has passed.

### Step 1: Find the cooling constant \( k \)
From the problem, we know:
- \( T_0 = 196^\circ \) (initial temperature),
- \( T_{\text{room}} = 70^\circ \),
- After 12 minutes, \( T(12) = 159^\circ \).

We can use the known values at \( t = 12 \) to find the constant \( k \). The equation for the temperature at \( t = 12 \) is:

\[
159 = 70 + (196 - 70) e^{-12k}
\]

### Step 2: Find the temperature at \( t = 25 \) minutes
Once \( k \) is determined, we can use the equation to find \( T(25) \).

Let me calculate the solution for you.The temperature of the coffee 25 minutes after being removed from the microwave is approximately **131 degrees** Fahrenheit.

Would you like further details or explanations on how this was solved?

Here are 5 related questions to deepen your understanding:

1. How does Newton's Law of Cooling relate to real-life temperature changes?
2. Why is it necessary to find the cooling constant \( k \) in problems like this?
3. How does the surrounding room temperature affect the cooling process?
4. How would the answer change if the room temperature was lower or higher?
5. Can Newton's Law of Cooling be applied to heating processes as well?

**Tip**: The rate of cooling depends on the difference between the object's temperature and the ambient temperature. The larger the difference, the faster the object cools!

A cup of coffee is removed from a microwave. Its initial temperature is 196 degrees. After exactly 12 minutes, it has cooled to 159 degrees. Assuming that the room temperature is 70 degrees, find the temperature of the coffee exactly 25 minutes after it is removed from the microwave. ROUND TO THE NEAREST DEGREE.

Solve a real-world problem involving Newton's Law of Cooling, where a cup of coffee cools from 196°F to 159°F in 12 minutes at room temperature (70°F). Find the coffee temperature after 25 minutes with detailed steps.

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