Final answer:
Without a specific cooling rate, the time for a pastry to cool from 150°F to 70°F cannot be calculated precisely; it requires monitoring the temperature according to food safety guidelines. Safe food handling practices are vital in preventing bacterial growth during the cooling process.
Step-by-step explanation:
The student's question involves determining the additional time required for a pastry to cool down to a safe consumption temperature in a refrigerator, specifically from 150°F to 70°F, after it has already cooled from 165°F to 150°F in 10 minutes. This type of problem generally falls under the category of exponential decay in mathematics and can often be solved using Newton's Law of Cooling. However, without a specific rate of cooling provided, a precise mathematical formula cannot be applied here. Instead, the answer could be estimated based on the rate of cooling observed thus far if we assume a linear relationship, but this would not provide an accurate model for how cooling typically progresses in food items. Given the limited data provided, and in order to maintain food safety, one should closely monitor the pastry's temperature and follow recommended food safety guidelines.
It is essential to understand that foods meant to be eaten cold should be refrigerated until served to prevent bacterial growth. A refrigerator should be kept at or below 4 degrees C (40 degrees F), and perishable leftovers should be refrigerated as soon as possible. Furthermore, as the pastry cools in the refrigerator, maintaining a proper temperature is critical to inhibit bacterial growth and ensure the food is safe to consume when it reaches the desired temperature of 70°F.