The domain of a function is the complete set of possible values of the variable that the function can accept. In this case, we are considering the function [tex]\( H(t) \)[/tex], which represents the height of a model rocket as a function of the time since it was launched, where [tex]\( t \)[/tex] represents time.
1. Understanding the Context:
- The function [tex]\( H(t) \)[/tex] describes the height of the rocket over time.
- The time [tex]\( t \)[/tex] represents the time since the launch of the rocket.
2. Physical Constraints:
- Since the rocket cannot be launched at a negative time, [tex]\( t \)[/tex] must represent non-negative values. Therefore, [tex]\( t \)[/tex] starts from [tex]\( 0 \)[/tex] and increases from there.
- There isn't an explicit upper limit to the time in the problem statement indicating when the rocket falls back to the ground or when other events might happen. So, we assume that the rocket can continue to exist in the context of the problem for as long as possible.
3. Definition of the Domain:
- The domain of [tex]\( H(t) \)[/tex] begins at [tex]\( t = 0 \)[/tex], the time of the rocket's launch.
- The absence of any specific upper limit in the problem statement allows us to consider any value of [tex]\( t \)[/tex] extending indefinitely into the future. Thus, [tex]\( t \)[/tex] can theoretically increase without bound.
Therefore, the domain of [tex]\( H(t) \)[/tex] is:
[tex]\[
\boxed{[0, \infty)}
\][/tex]
