In this scenario, we are modeling the population of a swarm of mosquitoes over time with the equation \( n(t) = 50(1.2)^t \), where \( n \) represents the number of mosquitoes after \( t \) days.
Since the city decides to spray for mosquitoes after 11 days, the domain for \( t \) should represent this time period, starting from day 0 (the beginning of the observation) up to day 11 (the day spraying starts).
Thus, the appropriate domain for \( t \) is:
\[ 0 \leq t \leq 11 \]
This captures the relevant time frame in which the mosquito population is being modeled before the intervention of spraying.
The other options provided do not accurately represent the situation. The first option (0<=n<=11) incorrectly restricts the number of mosquitoes, and the second option (0<=n<=372) is not relevant because it sets an arbitrary limit on populations. The third option (0<=t<=372) exceeds the time frame of interest.
Therefore, the correct choice is:
0 <= t <= 11
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