Question

The developing economies' share of the global gross domestic product (GDP) from 2003 to 2017 is shown in the following table. Year Share (% of GDP) Year Share (% of GDP) 2003 20 2011 35 2004 22 2012 38 2005 23 2013 39 2006 27 2014 40 2007 28 2015 41 2008 31 2016 42 2009 31 2017 43 2010 33 (a) Find the quadratic function that best models the developing economies' share of the global GDP as a function of the number of years after 2000. (Round all numerical values to four decimal places.) y(x) = ? (b) The model predicts that in the year 2027 , developing economies reach their maximum share, what %, of the GDP.

Answer 1

Solution-

Quadratic regression equation,

$y =ax^2+bx+c$

taking x = input/independent variable = year - 2000

and y = output/dependent variable = share of the global GDP

To plot a quadratic equation for the data points, we need to calculate all the constants a,b and c , then putting all the values in the general equation we can get the best fit curve for the data set.

Using, the graphing calculator, we can calculate the values of a, b, and c. The values were found to be,

a = -0.0471

b = 2.6366

c = 12.1001

Putting all the values,

$y =-0.0471x^2+2.6366x+12.1001$

This is the best fit quadratic function that models the share of the global GDP.

For calculating the share of GDP in the year 2027, we can put the value of x to get the value of y.

x = year-2000=2027-2000=27,

$y=-0.0471(27)^2+2.6366(27)+12.1001=-0.0471(729)+2.6366(27)+12.1001=48.95$

∴ In the year 2027, the maximum share will be 48.95% of total GDP.