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A loaf of bread is removed from an oven at 350° F and cooled in a room whose temperature is 70° F. If the bread cools to 210° F in 20 minutes, how much longer will it take for the bread to cool to 185° F?

Answer :

Final answer:

To calculate how much longer it will take the bread to cool to 185° F, we can use Newton's law of cooling.

Explanation:

To calculate how much longer it will take the bread to cool to 185° F, we can use Newton's law of cooling. Newton's law of cooling states that the rate of change of the temperature of an object is proportional to the difference between the object's temperature and the surrounding temperature. In this case, we can write the equation: (T - 70) = (350 - 70) * e^(kt), where T is the temperature of the bread at any given time, k is the cooling constant, and t is the time in minutes. We can rearrange the equation and solve for t when T = 185: t = ln((185 - 70) / (350 - 70)) / k.

Plugging in the values, we get: t = ln(115/280) / k. We know that it took 20 minutes for the bread to cool from 350° F to 210° F, so we can substitute that value into the equation: 20 = ln(140 / 280) / k. Solving for k, we get: k = ln(2) / 20. Now we can substitute this value of k back into our equation for t to find out how much longer it will take for the bread to cool to 185° F.

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