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A roast turkey is taken from an oven when its temperature has reached $ 185^{\circ}F $ and is placed on a table in a room where the temperature is $ 75^{\circ}F $. The graph shows how the temperature of the turkey decreases and eventually approaches room temperature. By measuring the slope of the tangent, estimate the rate of change of the temperature after an hour.

$-0.75^{\circ} \mathrm{F} / \mathrm{min}$

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What is a temperature?

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Temperature is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy, present in all matter, which is the source of the occurrence of heat, a flow of energy, when a body is in contact with another that is colder. I ho

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What is slope of a tangent?

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Hey Julia i know this one! You can determine the slope of a tangent line at any point on a function using calculus. By definition, the derivative of a function at any given point is equal to the slope of the tangent at that point. This value is also somet

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This would be easy Doug. The Fahrenheit scale is a temperature scale based on one proposed in 1724 by the physicist Daniel Gabriel Fahrenheit (1686–1736). It uses the degree Fahrenheit (symbol: °F) as the unit. Several accounts of how he originally defin

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Calculus: Early Transcedentals has kept me up at night until I found this

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Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

were asked to answer a question about turkey roasting using derivatives and rate of change. We're told that a roast turkey has taken from an oven when its temperature has reached 185 F and is placed on a table in a room where the temperature is 75 F. Were given a graph that shows how the temperature of turkey decreases and eventually approach his room temperature are asked to estimate the rate of change of the temperature after an hour by measuring the slope of the tangent to this graph. So to measure the slope of the tangent, Oregon D defined two points on the tangent line a little bit hard to see. This graph is quite small, however. Zoom in as best as you can from the glass graph. You can maybe gleam the points Let's say 25 150. And on the other side of the point of tangent C maybe 95 100 and therefore we have that the rate of change around the 60 minute mark is approximately the slope of the secret line. Em at this point, which we see is equal to about 100 minus 150 over 95. Minus 25. Simplifies to negative. 50 over 70 or negative 5/7. Of course, it really does depend on what points you used to approximate the slope of the tangent line. But the units, well, the Y axis, the units are degrees Fahrenheit. So this is negative 57 degrees Fahrenheit on the X axis, the units are minutes. This is negative 57 F per minute.

Ohio State University