To determine the population 3 years after the population started being recorded, we can use the given exponential function:
[tex]\[
p(x) = 2400(1.025)^x
\][/tex]
where [tex]\( x \)[/tex] represents the number of years since the population started being recorded. In this case, we need to find [tex]\( p(3) \)[/tex].
We will calculate the population 3 years after the initial time period by substituting [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
p(3) = 2400(1.025)^3
\][/tex]
Using the given calculations, we find:
[tex]\[
p(3) \approx 2584.54
\][/tex]
Approximately, the population 3 years after the start is about 2,584 people.
Therefore, the correct answer is:
C. 2,584 people
