To determine the domain of the function [tex]\(H(t)\)[/tex] that describes the height of a model rocket since its launch, we need to consider the following:
1. Launch Time: The rocket is launched at [tex]\( t = 0 \)[/tex]. Therefore, [tex]\( t \)[/tex] starts from 0.
2. Height Function Limits: The domain of [tex]\( H(t) \)[/tex] should cover the entire time period during which the model rocket's height is defined. This generally spans from the launch time until the rocket reaches the ground. Once the rocket reaches the ground for the first time, the height is no longer interesting or meaningful in most common scenarios.
Given the options, the best choice is the time span where the height of the rocket is defined:
- Option D: [tex]\( 0 \leq t \leq 34 \)[/tex] makes the most sense because it gives a specific end time for the rocket's flight. This means we have a defined period where the height can be measured, starting from launch (0) to when it lands (34).
Thus, the domain of [tex]\( H(t) \)[/tex] is [tex]\( 0 \leq t \leq 34 \)[/tex].
So, the correct answer is:
D. [tex]\( 0 \leq t \leq 34 \)[/tex]
