Certainly! To determine the population of the community 3 years after it started being recorded, we need to use the given exponential function for population growth:
[tex]\[ p(x) = 2400 \cdot (1.025)^x \][/tex]
Here,
- [tex]\( x \)[/tex] is the number of years since the population started being recorded.
- [tex]\( 2400 \)[/tex] is the initial population.
- [tex]\( 1.025 \)[/tex] is the growth rate per year.
Since we want the population after 3 years, we set [tex]\( x = 3 \)[/tex]:
[tex]\[ p(3) = 2400 \cdot (1.025)^3 \][/tex]
First, we need to calculate [tex]\( (1.025)^3 \)[/tex]:
[tex]\[ (1.025)^3 \approx 1.077 \][/tex]
Now, multiply this result by the initial population of 2400:
[tex]\[ p(3) = 2400 \cdot 1.077 \][/tex]
This gives us:
[tex]\[ p(3) \approx 2584.5375 \][/tex]
Rounding to a whole number, the population after 3 years is approximately:
[tex]\[ 2584 \][/tex]
So, the correct answer is:
[tex]\[ \text{B. 2,584 people} \][/tex]
