Question

The population of a swarm of mosquitos is growing at an exponential rate. The growth can be modeled by the equation n(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.(1 point)
Responses

0≤n≤11
0 less-than-or-equal-to n less-than-or-equal-to 11

0≤t≤11
0 less-than-or-equal-to t less-than-or-equal-to 11

0≤n≤372
0 less-than-or-equal-to n less-than-or-equal-to 372

0≤t≤372

Answer 1

In this scenario, the variable \( t \) represents time in days, and the mosquito population \( n(t) \) is modeled by the equation \( n(t) = 50(1.2)^t \).

Since you are interested in the number of days until the city decides to spray, and you want to define an appropriate domain for \( t \), you should consider that \( t \) represents the number of days, starting from 0 up to 11 days, as this is when the spraying occurs.

Thus, the appropriate domain for the situation is:

\[ 0 \leq t \leq 11 \]

So the correct response is:

**0 ≤ t ≤ 11**