Stitz-Zeager_College_Algebra_e-book

While we could plot a few points randomly a more

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Unformatted text preview: nce between the temperature of the coffee and its surroundings. Note in Equation 6.6 that the constant k is positive for both the cooling and warming scenarios. What determines if the function T (t) is increasing or decreasing is if T0 (the initial temperature of the object) is greater than Ta (the ambient temperature) or vice-versa, as we see in our next example. Example 6.5.4. A 40◦ F roast is cooked in a 350◦ F oven. After 2 hours, the temperature of the roast is 125◦ F. 1. Assuming the temperature of the roast follows Newton’s Law of Warming, find a formula for the temperature of the roast T as a function of its time in the oven, t, in hours. 2. The roast is done when the internal temperature reaches 165◦ F. When will the roast be done? Solution. 1. The initial temperature of the roast is 40◦ F, so T0 = 40. The environment in which we are placing the roast is the 350◦ F oven, so Ta = 350. Newton’s Law of Warming tells us T (t) = 350 + (40 − 350)e−kt , or T (t) = 350 − 310e−kt . To determine k...
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