To determine the appropriate domain for the problem, we need to focus on the variable \( t \), which represents time in hours. Since the scientist is observing the bacteria for a duration of 4 hours, the relevant range for \( t \) is from 0 to 4.
Now let's evaluate the options:
- Option #1: \( 0 \leq t \leq 104 \) - This includes values far beyond what the scientist is checking, which is not relevant here.
- Option #2: \( 0 \leq n \leq 104 \) - This describes the population of bacteria, but it is not specifically about the time variable \( t \).
- Option #3: \( 0 \leq t \leq 4 \) - This directly corresponds to the time period during which the scientist is observing the bacteria and is completely appropriate.
- Option #4: \( 0 \leq n \leq 4 \) - Similarly, this describes a range for the number of bacteria but is not relevant to the time variable.
Thus, the correct option reflecting the appropriate domain for \( t \) in this context is:
Option #3: \( 0 \leq t \leq 4 \).