Question

help i guess thanks
!

Answer 1

The population of the settlement that starts 26 people can be

expressed as a function g(x), similar to f(x).

Correct responses:

Part A

• The ways of expressing their populations represent functions because the population for each year is unique for the year

Part B

• Population of nearby community, f(x) > Population of other community, g(x) when; $0< x <29\frac{9}{79}$

• g(x) > f(x) when $x > 29\frac{9}{79}$

Reasons

Given:

The number of people that started the settlement in "Year Zero" are 26

people.

The average rate at which the population increases in a year = 2.6

people per year.

The function that describes the population in the nearby community, f(x),

given by the number of years from "year zero" is f(x) = -5.3·x + 256

Part A

A function is the rule that governs the relationship between two

variables, in which an input variable to the function, x, known as the

independent variable, determines the output variable, y, which is the

dependent variable.

In a function, therefore;

• Each input variable (x-value) has exactly one output variable (y-value).

The function that gives the population of the settlement that starts with 26 people is therefore;

g(x) = 26 + 2.6·x

Where;

x = The number of years from "year zero"

• Both communities ways of expressing their population represent functions because, each value of the input variable x gives a unique value of f(x) and g(x)

Part B

The population, f(x) = -5.3·x + 256 at year zero is f(0) = -5.3 × 0 + 256 = 256

The population, g(x) at "Year Zero" is 26

Therefore, at year zero, f(x) > g(x)

When the populations are equal, we have;

-5.3·x + 256 = 2.6·x + 26

2.6·x + 5.3·x = 256 - 26 = 230

7.9·x = 230

$x = \dfrac{230}{7.9} \approx \mathbf{29.114}$

Therefore;

• $f(x) > g(x) \ if \ 0 < x < \dfrac{230}{7.9}$

On the 30th year, we have;

f(30) = -5.3 × 30 + 256 = 97

g(x) = 2.6 × 30 + 26 = 104

Therefore,

• $g(x) > f(x) \ if \ x > \dfrac{230}{7.9}$

Therefore;

• Before, the 29.114 th year, the population that started with 256 people is larger than the population of the community that started with 26 people.

• After approximately 29 years, the population that started with 26 people becomes greater than the population that has 256 people at "Year Zero"

Learn more about functions here:

https://brainly.com/question/10687170