Calculate the average rate of change in the weight over the interval [8, 24]

To calculate the average rate of change in the man's weight \( W \) over the interval \([8, 24]\), we use the same formula for the average rate of change:

\[
\text{Average rate of change} = \frac{W(x_2) - W(x_1)}{x_2 - x_1}
\]

For the interval \([8, 24]\):
- \(x_1 = 8\), \(x_2 = 24\)
- \(W(x_1) = 54\), \(W(x_2) = 163\)

Substitute these values into the formula:

\[
\text{Average rate of change} = \frac{W(24) - W(8)}{24 - 8} = \frac{163 - 54}{24 - 8}
\]

Simplify the expression:

\[
\text{Average rate of change} = \frac{109}{16} \approx 6.81
\]

Thus, the average rate of change in weight over the interval \([8, 24]\) is **6.81 pounds per year**.

Would you like to explore more on this topic or have any questions?

Here are some related questions you might consider:
1. How would the average rate of change differ over the interval \([12, 20]\)?
2. What could be the possible reasons for the difference in the rate of change over different intervals?
3. Can the data be used to estimate the man's weight at other ages using linear interpolation or extrapolation?
4. How does the average rate of change help in understanding the growth pattern of weight over time?
5. How would you calculate the instantaneous rate of change in weight at a specific age?

**Tip:** The average rate of change gives a broad overview of how a quantity changes over a specified interval. It is particularly useful for comparing changes over different intervals.

Learn how to calculate the average rate of change in a person's weight over the interval [8, 24] with step-by-step guidance. This problem involves calculus concepts, specifically the average rate of change formula. Suitable for Grades 11-12.

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