Question

select the correct answer.
the population of a community, ( p(x) ), is modeled by this exponential function, where ( x ) represents the number of years since the population started being recorded.
( p(x) = 2,400(1.025)^x )
what is the approximate population 3 years after the population started being recorded?
a. 14,887 people
b. 2,460 people
c. 2,584 people
d. 7,380 people

Explanation:

Step1: Identify the value of x

We need to find the population 3 years after recording starts, so \( x = 3 \).

Step2: Substitute x into the function

The population function is \( p(x)=2400(1.025)^x \). Substitute \( x = 3 \):
\( p(3)=2400(1.025)^3 \)

Step3: Calculate \( (1.025)^3 \)

First, calculate \( 1.025\times1.025 = 1.050625 \), then \( 1.050625\times1.025 \approx 1.076890625 \)

Step4: Multiply by 2400

\( p(3)=2400\times1.076890625 \approx 2400\times1.076890625 = 2584.5375 \approx 2584 \)

Answer:

C. 2,584 people