(3.10) Linear Approximation 1. Thomas is roasting a 14 lb turkey as a test run f
ID: 2888605 • Letter: #
Question
(3.10) Linear Approximation 1. Thomas is roasting a 14 lb turkey as a test run for Thanksgiving. He starts roasting the turkey at noon. At 1:00pm, he checks on the turkey using a fancy thermometer, and he discovers that it has an internal temperature of 35.6°C, and its temperature is rising at an instantaneous rate of 0.25°C per minute a) Approximate the temperature of the turkey at 1:06pm (b) Let I(t) be the turkey's internal temperature (in °C) t minutes after noon. Identify, using func- tional notation, the two pieces of information you were given about the turkey.Explanation / Answer
a) The current temperature at 1pm is 35.6 degrees and is rising at 0.25 degrees per minute (an approximation of linear rise);
So at 1:06 pm, after 6 minutes of rise, the temperature is expected to be = 35.6 + 6(0.25) = 35.6 + 1.5 = 37.1 degrees;
Thus, the approximate temperature at 1:06pm is = 37.1 degrees
b) The two pieces of information we have been given about the turkey with respect to I (t) is
At 1:00pm, I (t) = I (60) = 35.6 degrees
And at t=60, d I(t) / dt = 0.25 degrees/ minute
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.