Question

A roast turkey is 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.

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 1

It is very important to look at the graph very minutely. It can be seen that at 30 minutes the slope is a little more than negative 50 and at 90 minutes it is a little less than negative 50. From this fact, it can be deduced that the estimated rate of change of the temperature after an hour would be -50/60. I hope that the answer has come to your desired help.

Answer 2

Slope of the line indicates the direction and the steepness of the line.

The rate of change of the temperature of roast is changing(decreasing) 40 degrees Fahrenheit per hour.

What is the slope of the line?

Slope of the line indicates the direction and the steepness of the line. It can be given as,

$m=\dfrac{y_2-y_1}{x_2-x_1}$

Here, $x,y$ are the coordinate points on which the line passes through.

Given information-

The initial temperature of roast is  185°F.

The temperature of room is 75°F.

The tangent line in the given graph passes through the one points (30,145).

The another point of the tangent line are (90,105).

As the two point of the curve we have. Thus the slope of the line passing through the point (30,145). and (90,105) can be given as,

$m=\dfrac145-105{}{30-90}\\m=\dfrac{40}{-60}\\m\cong-0.667\rm F^o/min$

For an hour,

$m=-0.667\times60\\m=-40\rm F^o/min$

Thus the rate of temperature of is changing 40 degrees Fahrenheit each hour. Here the negative sign indicates that the temperature of roast is decreasing with time.

Hence the rate of change of the temperature of roast is changing(decreasing) 40 degrees Fahrenheit per hour.

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