Find the rate of change between t = 1.5 and t = 2.5 seconds

To find the rate of change between \( t = 1.5 \) seconds and \( t = 2.5 \) seconds, we'll use the same formula:

\[
\text{Rate of Change} = \frac{\text{Change in Height}}{\text{Change in Time}}
\]

From the table:

- At \( t = 1.5 \) seconds, the height is 164 feet.
- At \( t = 2.5 \) seconds, the height is 100 feet.

Now, calculate the rate of change:

\[
\text{Rate of Change} = \frac{100 - 164}{2.5 - 1.5} = \frac{-64}{1.0} = -64 \text{ feet per second}
\]

The rate of change between \( t = 1.5 \) and \( t = 2.5 \) seconds is \(-64\) feet per second.

Would you like more details on this calculation or have any questions?

Here are some related questions to consider:
1. How does the rate of change between \( t = 1.5 \) and \( t = 2.5 \) seconds compare to the rate of change between \( t = 1.5 \) and \( t = 2.0 \) seconds?
2. What might a larger interval of time tell us about the overall behavior of the height function?
3. How would you calculate the rate of change over the entire time interval from \( t = 0.0 \) to \( t = 2.5 \) seconds?
4. What does the rate of change suggest about the motion of the object between these time intervals?
5. How could you determine if the object's speed is constant or changing over time?

**Tip:** When comparing rates of change over different intervals, it's helpful to consider the context of the problem to interpret whether the changes suggest acceleration, deceleration, or constant speed.

Learn how to calculate the rate of change between t = 1.5 seconds and t = 2.5 seconds using the formula Rate of Change = (100 - 164) / (2.5 - 1.5). Understand the implications of negative rate of change and its application in analyzing motion and functions. Suitable for high school students.

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