Final answer:
To find the temperature of the body after the next 7 minutes, we can use Newton's Law of cooling. Using the given data, we can calculate the cooling constant (k) and then use it to find the temperature of the body after 7 minutes. The temperature of the body after 7 minutes is approximately 27.05°C.
Step-by-step explanation:
To determine the temperature of the body after the next 7 minutes, we can use Newton's Law of cooling. According to Newton's Law of Cooling, the rate of change of temperature of an object is proportional to the difference between its temperature and the temperature of its surroundings.
In this case, the initial temperature of the body is 40°C and the temperature of the surroundings is 10°C. Since the body cools from 60°C to 40°C in 7 minutes, we can calculate the cooling constant (k) using the formula:
k = (ln((60 - 10) / (40 - 10))) / 7
Solving this equation gives us a value of k ≈ -0.06731.
Now, we can use the value of k to find the temperature of the body after the next 7 minutes:
Temperature after 7 minutes = 10 + (40 - 10) * e^(k * 7)
Calculating this equation, we find that the temperature of the body after the next 7 minutes is approximately 27.05°C.