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Problem 46 Medium Difficulty

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.

Answer

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

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June 8, 2020

SH

Sarah H.

September 22, 2020

What is a temperature?

EV

Eric V.

September 22, 2020

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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Julia M.

September 22, 2020

What is slope of a tangent?

EG

Erica G.

September 22, 2020

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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Doug F.

September 22, 2020

What is the term Fahrenheit?

BS

Brad S.

September 22, 2020

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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October 22, 2020

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October 23, 2020

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A Ferris wheel of radius 20 feet is rotating counterclockwise with an angular velocity of 1 radian per second. One seat on the rim is at (20,0) at time (a) What are its coordinates at (b) How fast is it rising (vertically) at (c) How fast is it rising

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October 18, 2021

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Video Transcript

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.