Question

the following table gives projections of the population of a country from 2000 to 2100.
answer parts (a) through (c).

year	population (millions)	year	population (millions)
2010	303.6	2070	470.4
2020	326.7	2080	506.3
2030	359.6	2090	538.6
2040	383.1	2100	574.5
2050	406.1

(a) find a linear function that models the data, with ( x ) equal to the number of years after 2000 and ( f(x) ) equal to the population in millions.
( f(x) = square x + square )
(type integers or decimals rounded to three decimal places as needed.)

Explanation:

Step1: Define variables and points

Let $x$ = years after 2000, $f(x)$ = population (millions). Use two points: $(0, 282.2)$ (2000) and $(10, 303.6)$ (2010).

Step2: Calculate slope $m$

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{303.6-282.2}{10-0}=\frac{21.4}{10}=2.14$

Step3: Find y-intercept $b$

When $x=0$, $f(0)=b=282.2$

Step4: Form linear function

Substitute $m$ and $b$ into $f(x)=mx+b$

Answer:

$f(x)=2.14x + 282.2$