Answered

Select the correct answer.

The population of a community, [tex][tex]$p(x)$[/tex][/tex], is modeled by this exponential function, where [tex][tex]$x$[/tex][/tex] represents the number of years since the population started being recorded.

[tex][tex]$p(x) = 2,400(1.025)^x$[/tex][/tex]

What is the approximate population 3 years after the population started being recorded?

A. 7,380 people
B. 14,887 people
C. 2,584 people
D. 2,460 people



Answer :

GinnyAnswer
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