A pan filled with hot food cools from `94^(@)C` to `86^(@)C` in 2 minutes when the room temperature is at `20^(@)C`. How long will it take to cool from `71^(@)C` to ` 69^(@)C`? Here cooling takes place according to Newton's law of cooling.

Explanation

To solve the problem using Newton's law of cooling, we can follow these steps:

### Step 1: Understand Newton's Law of Cooling
Newton's law of cooling states that the rate of change of temperature of an object is proportional to the difference between its temperature and the surrounding temperature. The formula can be expressed as:

\[ \frac{T_2 - T_1}{t} = k \left( \frac{T_1 + T_2}{2} - T_s \right) \]
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