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Blogmas Day 7

For the 7th day of Blogmas, I will discuss how long it will take Christmas cookies to cool to 75° F once they are taken out of the oven. For this calculation I will use Newton's Law of Cooling. This law states that the rate of cooling is proportional to the temperature difference between the object and its surroundings; therefore, dT/dt = k(T-TC) with Tc the constant temperature. To find this calculation, I first found Tc to be 70° F because my house temperature is kept at this constant. Next, I used the separation of differentiable equations method to integrate the Newton's Law of Cooling Equation. As a result, I found the equation to be T(t)= Ce^(kt) + 70. To find the value of C,I set Ce^(kt) equal to 350° F( the temperature of the cookies immediately after they were taken out of the oven) and set t=0. With this information, I found C to be 280. I measured the temperature of the cookies to be 300° F after 5 minutes. Using this information, k was measured to be -.0393. After finding all the unknowns, I finally found the time it takes to cool to 75° F to be 102 minutes.

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