To determine the domain of [tex]\( H(t) \)[/tex], we need to consider the context in which the function is defined and any possible constraints on the variable [tex]\( t \)[/tex].
1. Identify the Variable: The variable [tex]\( t \)[/tex] represents the time since the launch of a model rocket. Time is typically measured in non-negative units (seconds, minutes, etc.).
2. Analyze the Meaning: Since [tex]\( t \)[/tex] represents time, it can’t be negative. This means that [tex]\( t \)[/tex] must be a non-negative real number.
3. Define the Domain: The domain of [tex]\( H(t) \)[/tex] will include all possible values of [tex]\( t \)[/tex] for which [tex]\( H(t) \)[/tex] is defined. Since [tex]\( t \)[/tex] is the time elapsed since the launch, and time can start from 0 and extend indefinitely into the future, the domain of [tex]\( t \)[/tex] will be all non-negative real numbers.
Therefore, the domain of [tex]\( H(t) \)[/tex] is given by:
[tex]\[
t \geq 0
\][/tex]
In interval notation, this can be written as:
[tex]\[
[0, \infty)
\][/tex]
Hence, the domain of [tex]\( H(t) \)[/tex] is [tex]\((0, \text{inf})\)[/tex].
