Question

A roasted turkey is taken from an oven when its temperature has reached 175 Fahrenheit and is placed on a table in a room where the temperature is 70. Fahrenheit. Give answers accurate to at least 2 decimal places. If the temperature of the turkey is 150 Fahrenheit after half an hour, what is its temperature after 35 minutes?

Answer 1

To find the temperature of the turkey after 35 minutes, we can use Newton's Law of Cooling. Solving the equation, we find that the temperature is approximately 152.12 Fahrenheit.

Step-by-step explanation:

To solve this problem, we can use Newton's Law of Cooling which states that the rate of change of temperature of an object is proportional to the difference between the temperature of the object and its surroundings. The equation for this law is given by:

T(t) = T0 + (T1 - T0)e^(-kt)

where T(t) is the temperature of the object at time t, T0 is the initial temperature of the object, T1 is the temperature of the surroundings, and k is the cooling constant.

In this case, T0 is 175F, T1 is 70F, and the time difference between the initial temperature and the temperature after half an hour is 30 minutes. We can plug these values into the equation to find the cooling constant:

150 = 175 + (70 - 175)e^(-30k)

Solving this equation, we find that k is approximately -0.00949. Now we can use this value to find the temperature after 35 minutes:

T(35) = 175 + (70 - 175)e^(-0.00949 * 35) = 152.12 Fahrenheit

Learn more about Newton's Law of Cooling