Question

the table gives the projections of the population, in millions, of a countrys residents over age 16 for selected years from 2015 to 2060. answer parts (a) through (e).
year population (millions) year population (millions)
2015 255.161 2040 306.634
2020 266.024 2045 315.152
2025 276.558 2050 323.314
2030 286.967 2055 331.770
2035 297.259 2060 340.868
a. graph the data, with y equal to the population in millions and x equal to the number of years after 2010. choose the correct graph below. all graphs have viewing window 0, 60 by 0, 400 with xscl = 5 and yscl = 50.
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: Prepare data points

For 2015 ($x = 5$), $y=255.161$; for 2020 ($x = 10$), $y = 266.024$; for 2025 ($x = 15$), $y=276.558$; for 2030 ($x = 20$), $y=286.967$; for 2035 ($x = 25$), $y=297.259$; for 2040 ($x = 30$), $y=306.634$; for 2045 ($x = 35$), $y=315.152$; for 2050 ($x = 40$), $y=323.314$; for 2055 ($x = 45$), $y=331.770$; for 2060 ($x = 50$), $y=340.868$.

Step2: Calculate slope $m$

The slope formula for a line $y=mx + b$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points, say $(x_1,y_1)=(5,255.161)$ and $(x_2,y_2)=(50,340.868)$. Then $m=\frac{340.868 - 255.161}{50 - 5}=\frac{85.707}{45}\approx1.905$.

Step3: Calculate $y$-intercept $b$

Use the point - slope form $y - y_1=m(x - x_1)$ with the point $(5,255.161)$ and $m = 1.905$. So $y-255.161=1.905(x - 5)$. Expand to get $y-255.161=1.905x-9.525$. Then $y=1.905x+245.636$.

Answer:

a. (Since no graphs are described in detail here, assume the correct one is the one that matches the data points' trend. If we consider the increasing nature of the population data, we would need to visually check the graphs provided in the actual context).
b. $y = 1.905x+245.636$