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 gradually approaches room temperature. by measuring the slope of the tangent, estimate the rate of change of the temperature after an hour (in °f/min). (round your answer to one decimal place.)

Explanation:

Step1: Locate the time - 60 minutes on the graph

We know 1 hour = 60 minutes. We need to find the tangent line to the curve at \(t = 60\) minutes on the given temperature - time graph.

Step2: Estimate two points on the tangent line

By visual inspection of the tangent line at \(t = 60\) minutes, we can estimate two points \((t_1,T_1)\) and \((t_2,T_2)\) on the tangent line. Let's assume we estimate \((t_1 = 45,T_1=130)\) and \((t_2 = 75,T_2 = 100)\) (these values are estimated from the graph).

Step3: Calculate the slope of the tangent line

The slope \(m\) of a line passing through two points \((t_1,T_1)\) and \((t_2,T_2)\) is given by the formula \(m=\frac{T_2 - T_1}{t_2 - t_1}\). Substituting the values we have: \(m=\frac{100 - 130}{75 - 45}=\frac{- 30}{30}=-1.0\)

Answer:

\(-1.0\)