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To solve this problem, you need to estimate the **instantaneous change** (or rate of change) of the wind speed at hour 58. The best approach to estimate this using tabular data is to apply the **average rate of change** formula, which is:

\[
\frac{\Delta \text{Wind speed}}{\Delta t} = \frac{\text{Wind speed at time 2} - \text{Wind speed at time 1}}{t_2 - t_1}
\]

Here, we will calculate the rate of change around hour 58 using the data points at times that are as close as possible to hour 58. From the table:

- The wind speed at hour 49 is 145 mph.
- The wind speed at hour 73 is 155 mph.

So, we can estimate the rate of change using these two points:

\[
\frac{\Delta \text{Wind speed}}{\Delta t} = \frac{155 - 145}{73 - 49} = \frac{10}{24} \approx 0.4167 \, \text{mph per hour}
\]

Thus, the estimated instantaneous rate of change of the wind speed at hour 58 is **approximately 0.417 mph per hour**.

### Physical Meaning:
The value represents the **rate at which the wind speed is increasing** at hour 58. Specifically, the wind speed is increasing by approximately 0.417 mph every hour at that moment in time.

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Do you need more details or have any questions?

Here are 5 related questions to explore:
1. How is the instantaneous rate of change different from the average rate of change?
2. How would you estimate the rate of change if the data points were closer to hour 58?
3. What other methods could be used to estimate the instantaneous rate of change if more data were available?
4. How can this method be used to find the rate of change for other quantities, such as temperature or pressure?
5. What does it mean if the rate of change at a particular point is zero?

**Tip:** When dealing with tables of data, always look for points that are closest to the value you are interested in to estimate instantaneous changes accurately!

Using the table, estimate the instantaneous change of the wind speed at hour 58.

Learn how to estimate the instantaneous change of wind speed at hour 58 using tabular data for Hurricane Katrina in 2005. This problem involves calculating the rate of change using the average rate of change formula, covering key concepts in calculus. Suitable for students in Grades 11-12 and college level.

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