Determine the temperature of the turkey after 45 minutes given its temperature after 30 minutes: A roasted turkey is taken from an oven when its temperature has reached 185 Fahrenheit and is placed on a table in a room where the temperature is 75 Fahrenheit. Give answers accurate to at least 2 decimal places. (a) If the temperature of the turkey is 143 Fahrenheit after half an hour, what is its temperature after 45 minutes? Fahrenheit (b) When will the turkey cool to 100 Fahrenheit? hours. Question Help: $\square$ Video

Step 1 ：Given that the initial temperature of the turkey (\(T_0\)) is 185 Fahrenheit, the ambient temperature (\(T_s\)) is 75 Fahrenheit, and the temperature of the turkey after 30 minutes (\(T_{30}\)) is 143 Fahrenheit.

Step 2 ：We can use these values in the formula for Newton's Law of Cooling, which is \(\frac{dT}{dt} = -k(T - T_s)\), to find the value of the cooling constant (\(k\)).

Step 3 ：By substituting the given values into the formula, we get \(k = 0.01603242202054365\).

Step 4 ：Now that we have the value of \(k\), we can use it to find the temperature of the turkey after 45 minutes (\(T_{45}\)).

Step 5 ：Substituting the values of \(k\), \(T_0\), \(T_s\), and \(t = 45\) minutes into the formula, we get \(T_{45} = 128.46468673126896\) Fahrenheit.

Step 6 ：Rounding to two decimal places, the temperature of the turkey after 45 minutes is approximately \(\boxed{128.46}\) Fahrenheit.