Question

Richard removes a turkey from the oven after it reaches a temperature of 178◦F and places on a table in his dining room where the temperature is 60◦F. After 10 minutes the temperature of the turkey is 162◦F, while after 20 minutes it is 152◦F. Use linear approximation to predict the temperature of the turkey after half an hour.

Answer 1

Using linear approximation, we predict that the temperature of the turkey will be approximately 151◦F after half an hour.

Step-by-step explanation:

To use linear approximation to predict the temperature of the turkey after half an hour, we can assume that the temperature change is approximately linear over the given time period.

We know that after 10 minutes, the temperature of the turkey is 162◦F, and after 20 minutes, it is 152◦F. Therefore, the temperature change over this time interval is -10◦F (162◦F - 152◦F).

Since the temperature change is assumed to be linear, we can approximate the rate of temperature decrease as -10◦F per 10 minutes, or -1◦F per minute.

Now, to predict the temperature after half an hour (30 minutes), we can use the linear approximation by assuming a consistent rate of temperature decrease.

From the initial temperature of 178◦F to the temperature after 20 minutes (152◦F), the temperature has decreased by 26◦F (178◦F - 152◦F).

Using the rate of temperature decrease of -1◦F per minute, we can estimate that in the next 10 minutes (from 20 to 30 minutes), the temperature will decrease by an additional -1◦F.

Therefore, the predicted temperature after half an hour (30 minutes) would be 152◦F - 1◦F = 151◦F.

Answer 2

To predict the temperature of the turkey after half an hour, we can use linear approximation. The rate of change of temperature is calculated using the temperatures at different time intervals. Using this rate of change, we can predict the temperature after half an hour.

Step-by-step explanation:

To predict the temperature of the turkey after half an hour, we can use linear approximation. We have the temperature of the turkey at two different time intervals: after 10 minutes it is 162°F, and after 20 minutes it is 152°F.

We can find the rate of change of temperature by subtracting the initial temperature from the final temperature and dividing it by the time interval. So, the rate of change of temperature is (162°F - 178°F) / 10 minutes = -1.6°F per minute.

Using this rate of change, we can predict the temperature after half an hour (30 minutes). The change in temperature would be -1.6°F/minute * 30 minutes = -48°F. Subtracting this change from the initial temperature, we get the predicted temperature: 178°F - 48°F = 130°F.