Question

The table shows data from 1975 and projections to 2050 of the number of millions of people age 15 to 59 in a large country. Complete parts (a) and (b) below. EEClick the icon to view the data table. a function of the number What is the quadratic function that best models this population years after 1970? Let x represent the number of years after 1970 and y represent the number of millians of people in this labor pool. y i Labor Pool (Type an equation. Type integers or decimals rounded to three decimal places for any numbers. the equation.) Labor Pool (milllons) 917 Labor Pool (millions) Year Year 1975 487 2015 924 1980 555 2020 1985 646 2025 909 2 1995 2000 796 820 2040 800 2005 871 2045 2010 670 913 2050

Answer 1

Let quadratic function is y = a + b x + c x^2 rightwardsdoublearrow epsilon y = h a + b epsilon x + c epsilon x^2 epsilon x y = a epsilon x + b epsilon x^2 + c epsilon x^3 epsilon x^2 y = a epsilon x^2 + b epsilon x^3 + c epsilon x^4 rightwardsdoublearrow 12495 = 16a + 680 b + 37400 c 556655 = 680 a + 37400 b + 2312000 c 30581575 = 37400 a + 2312000 b + 152405000 On solving rightwardsdoublearrow a = 366.073 b = 22.132 c = -0.225 Therefore y = 366.073 + 22.132 times - 0.225 x^2