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Answer :
To calculate the time it takes for the cake to cool to 90 degrees Fahrenheit, we can use Newton's Law of Cooling. The cooling constant and time are calculated using the formula t = -(1/cooling constant) * ln((final temperature - room temperature)/(initial temperature - room temperature)). In this case, it will take approximately 28.63 minutes for the cake to cool to 90 degrees Fahrenheit.
To calculate the time it takes for the cake to cool to 90 degrees Fahrenheit, we can use Newton's Law of Cooling. First, we need to calculate the cooling constant, which is the difference between the initial and final temperature divided by the natural logarithm of the ratio of the initial and final temperatures. In this case, the initial temperature is 350 degrees Fahrenheit, the final temperature is 90 degrees Fahrenheit, and the room temperature is 65 degrees Fahrenheit. Plugging in these values, we find the cooling constant to be approximately -0.073.
Next, we can use the cooling constant to find the time it takes for the cake to cool to 90 degrees Fahrenheit. The general formula for Newton's Law of Cooling is t = -(1/cooling constant) * ln((final temperature - room temperature)/(initial temperature - room temperature)). Substituting the values, we find that it takes approximately 28.63 minutes for the cake to cool to 90 degrees Fahrenheit.
Therefore, it will take approximately 28.63 minutes for the cake to cool to 90 degrees Fahrenheit.
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