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Find the rate of change between t = 1.5 and t = 2 seconds 

To find the rate of change between \( t = 1.5 \) seconds and \( t = 2.0 \) seconds, we can use the following formula for the average rate of change:

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

From the table:

- At \( t = 1.5 \) seconds, the height is 164 feet.
- At \( t = 2.0 \) seconds, the height is 136 feet.

Now, calculate the rate of change:

\[
\text{Rate of Change} = \frac{136 - 164}{2.0 - 1.5} = \frac{-28}{0.5} = -56 \text{ feet per second}
\]

The rate of change between \( t = 1.5 \) and \( t = 2.0 \) seconds is \(-56\) feet per second.

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

Here are some related questions to consider:
1. What does the negative sign in the rate of change indicate?
2. How would you calculate the rate of change between \( t = 0.5 \) and \( t = 1.0 \) seconds?
3. Can you determine the overall trend of the object's height over time based on the rate of change?
4. How might you use this data to estimate the height at \( t = 3.0 \) seconds?
5. How would the rate of change differ if the time interval were larger?

**Tip:** When analyzing a rate of change, remember that a negative value indicates a decrease in the quantity being measured over the given interval.

Learn how to calculate the rate of change between t = 1.5 seconds and t = 2 seconds using the average rate of change formula. Understand the significance of negative rates of change and apply the calculation to real-world scenarios. Suitable for high school students.

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