the table gives the projections of the population, in millions, of a countrys residents over age 16 for…

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).\n| year | population (millions) | year | population (millions) |\n| ---- | ---- | ---- | ---- |\n| 2015 | 255.161 | 2040 | 306.634 |\n| 2020 | 266.024 | 2045 | 315.152 |\n| 2025 | 276.558 | 2050 | 323.314 |\n| 2030 | 286.967 | 2055 | 331.770 |\n| 2035 | 297.259 | 2060 | 340.868 |\nall graphs have viewing window 0, 60 by 0, 400 with xscl = 5 and yscl = 50.\nthe linear model is a very good fit for the data.\n d. what does the model predict that the population will be in 2042?

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).\n| year | population (millions) | year | population (millions) |\n| ---- | ---- | ---- | ---- |\n| 2015 | 255.161 | 2040 | 306.634 |\n| 2020 | 266.024 | 2045 | 315.152 |\n| 2025 | 276.558 | 2050 | 323.314 |\n| 2030 | 286.967 | 2055 | 331.770 |\n| 2035 | 297.259 | 2060 | 340.868 |\nall graphs have viewing window 0, 60 by 0, 400 with xscl = 5 and yscl = 50.\nthe linear model is a very good fit for the data.\n d. what does the model predict that the population will be in 2042?

Answer

Explanation:

Step1: Let (x = 0) represent the year 2015. Then for the year 2042, (x=2042 - 2015=27).

Since the linear - model is a very good fit for the data, assume the linear model is of the form (y = mx + b). We can use two points ((x_1,y_1)) and ((x_2,y_2)) from the data to find the equation of the line. Let's take ((x_1 = 0,y_1=255.161)) (corresponding to 2015) and ((x_2 = 25,y_2 = 297.259)) (corresponding to 2040). First, find the slope (m) using the formula (m=\frac{y_2 - y_1}{x_2 - x_1}). [m=\frac{297.259 - 255.161}{25-0}=\frac{42.098}{25}=1.68392] Since (y_1 = 255.161) and (x_1 = 0), the (y) - intercept (b = 255.161). So the linear model is (y=1.68392x + 255.161).

Step2: Substitute (x = 27) into the linear model.

[y=1.68392\times27+255.161] [y = 45.46584+255.161] [y=300.62684]

Answer:

300.627 (rounded to three decimal places)