Question

the table gives the projections of the population, in millions, of a country’s residents over age 16 for selected years from 2015 to 2060. answer parts (a) through (e).

year	population (millions)	year	population (millions)
2020	266.024	2045	315.152
2025	276.558	2050	323.314
2030	286.967	2055	331.770
2035	297.259	2060	340.868

b. find a linear function that models the data, with y equal to the population in millions and x equal to the number of years after 2010.

y = □x + □
(type integers or decimals rounded to three decimal places as needed.)

Explanation:

Step1: Define variables

Let \( x \) be years after 2010, so for year 2015, \( x = 2015 - 2010 = 5 \), and \( y = 255.161 \); for 2020, \( x = 10 \), \( y = 266.024 \).

Step2: Calculate slope \( m \)

Slope formula: \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using \( (5, 255.161) \) and \( (10, 266.024) \):
\( m=\frac{266.024 - 255.161}{10 - 5}=\frac{10.863}{5}=2.1726 \approx 2.173 \)

Step3: Find y-intercept \( b \)

Use point-slope form \( y - y_1 = m(x - x_1) \) with \( (5, 255.161) \):
\( y - 255.161 = 2.1726(x - 5) \)
\( y = 2.1726x - 10.863 + 255.161 \)
\( y = 2.1726x + 244.298 \approx 2.173x + 244.298 \)

Answer:

\( y = \boldsymbol{2.173}x + \boldsymbol{244.298} \)