The problem asks for the average rate at which the object falls during the first 3 seconds, using the given height function $h(t) = 300 - 16t^2$.

To find the average rate of change, we can use the formula:

$\text{Average rate of change} = \frac{h(t_2) - h(t_1)}{t_2 - t_1}$ Where:

• $t_1 = 0$ (the initial time)
• $t_2 = 3$ (after 3 seconds)

So, the average rate of change for the height during the first 3 seconds is: $\frac{h(3) - h(0)}{3 - 0}$ This expression corresponds to the option: $\frac{h(3) - h(0)}{3}$ which is the last choice in the list (the fourth option).

Would you like a detailed breakdown of the calculations, or do you have any other questions? Here are some related questions to consider:

1. What does the average rate of change represent physically in this context?
2. How do you calculate $h(3)$ and $h(0)$ from the given function?
3. How is the average rate of change different from the instantaneous rate of change?
4. What would happen if the object was dropped from a different height?
5. How can you interpret the negative sign in the rate of change?

Tip: The average rate of change over an interval gives the object's overall speed, while the instantaneous rate would tell you its exact speed at a given moment.