The population of a swarm of mosquitos is growing at an exponential rate. The growth can be modeled by the equationn(t)=〖50(1.2)〗^t, where n is the number of mosquitos after t days. After 11 days, a city decides to spray for mosquitos. Define an appropriate domain for the situation.

Answer 1

To define an appropriate domain for the situation described, we need to consider the context of mosquito population growth over time.

The equation provided for the mosquito population is:

\[ n(t) = 50(1.2)^t \]

where \( n(t) \) is the number of mosquitos after \( t \) days.

Key considerations for defining the domain:

1. Time: Since \( t \) represents the number of days, it should start from \( t = 0 \) (the initial time when the population is first considered). \( t \) should also only take non-negative values because negative days (before time zero) do not make sense in this context.

2. Length of observation: The problem states that after 11 days, the city decides to spray for mosquitos. Therefore, while the model could technically continue beyond 11 days, we should consider the practical scenario, especially if we want to analyze how the population behaves before intervention.

Given these considerations, the appropriate domain for \( t \) in this situation is:

\[ t \geq 0 \quad \text{(non-negative integers or real numbers)}
\]

If we're focusing on the period leading up to the spraying after 11 days, we can define a more specific domain:

\[ 0 \leq t \leq 11
\]

In conclusion, the most appropriate domain for the situation is:

\[ t \in [0, 11] \]

This indicates we are observing the mosquito population starting from day 0 up until day 11.