City planners anticipate an 8.2% population growth per year, including new residents and births. The population, in millions of people, based on this increase can be modeled by the function p(x) = 2.5(1.082), where x is the number of years of tracked growth. The planners also estimate a 3% population loss over the same time period that can be modeled by the function L(p) = p(0.97).

From the statement we know the function that models the population growth over the years (p(x)) but we have been told that there is an estimated loss that can be modeled by the function L(p), so in order to find which function represents the final function, we need to composite the function, which is the same that evaluate p(x) into the function L(p).

We are given:

[tex]p(x)=2.5(1.082)^{x}[/tex]

and

[tex]L(p(x))=p(0.97)[/tex]

So, the evaluationg p(x) into L(p), we have:

[tex]L(p(x))=p(0.97)\\\\L(p(x))=2.5(1.082)^{x}*(0.97)=0.97*2.5(1.082)^{x} \\\\L(p(x))=0.97*2.5(1.082)^{x}=2.425(1.082)^{x}\\\\L(p(x))=2.425(1.082)^{x}[/tex]

Hence, the correct option is:

The third option,

[tex]L(p(x))=2.425(1.082)^{x}[/tex]

Have a nice day!

jennifercadey jennifercadey · Answer 2 · 2020-12-12T22:51:33+01:00

jennifercadey jennifercadey

12-12-2020

Answer:

D) L(p(x)) = 2.5(1.04954)x

Step-by-step explanation:

Answer Link