To find the rate of change of the turkey's temperature after an hour, we need to determine the slope of the tangent line to the curve at $t = 60$ minutes. Here's how we can approximate this:

1. Locate the Point: At $t = 60$ minutes (point $P$ on the graph), we identify the temperature value on the curve. From the graph, it looks like the temperature is approximately 120°F.

2. Draw the Tangent: The problem suggests using the slope of the tangent line at this point. On the graph, we look for a line that just touches the curve at $t = 60$ minutes and estimate the change in temperature over a small time interval.

3. Estimate the Slope: The slope of the tangent can be found using the formula: $\text{slope} = \frac{\Delta T}{\Delta t},$ where $\Delta T$ is the change in temperature and $\Delta t$ is the change in time.

4. Approximation: By looking at the tangent line, we estimate the rate of temperature change. Suppose we approximate a fall of 20°F over a 50-minute interval around $t = 60$ (from approximately 140°F at $t = 50$ minutes to 120°F at $t = 100$ minutes).

   Then, $\text{slope} \approx \frac{-20 \, \text{°F}}{50 \, \text{min}} = -0.4 \, \text{°F/min}.$

So, the rate of change of the temperature after an hour is approximately -0.4°F/min.

Would you like a more detailed explanation or have any questions?

Here are some related questions for further exploration:

1. How does the rate of change vary at different times (e.g., after 30 minutes, 90 minutes)?
2. What is the long-term temperature of the turkey as time approaches infinity?
3. Can we model this cooling process using Newton's Law of Cooling?
4. How would a different room temperature affect the rate of cooling?
5. How can you use calculus to find the exact rate of change if the equation of the curve is known?

Tip: When estimating slopes on a graph, try to pick two points as far apart as possible on the tangent line to minimize error in the slope calculation.