Chapter 2.5, Problem 30E

Developing economies The developing economies’ share of the global gross domestic product (GDP) from $2003$ to $2017$ is shown in the following table.

Find the quadratic function that best models GDP as a function of the number of year after $2000$.

Use technology to find the maximum share of GDP that the developing economics can achieve, according to this model.

$\begin{array}{llll}\hfill & \text{Share}\hfill & \hfill & \text{Share}\hfill \\ \text{Year}\hfill & \text{(\% of GDP)}\hfill & \text{Year}\hfill & \text{(\% of GDP)}\hfill \\ \text{2003}\hfill & \text{20}\hfill & \text{2011}\hfill & \text{35}\hfill \\ \text{2004}\hfill & \text{22}\hfill & \text{2012}\hfill & \text{38}\hfill \\ \text{2005}\hfill & \text{23}\hfill & \text{2013}\hfill & \text{39}\hfill \\ \text{2006}\hfill & \text{27}\hfill & \text{2014}\hfill & \text{40}\hfill \\ \text{2007}\hfill & \text{28}\hfill & \text{2015}\hfill & \text{41}\hfill \\ \text{2008}\hfill & \text{31}\hfill & \text{2016}\hfill & \text{42}\hfill \\ \text{2009}\hfill & \text{31}\hfill & \text{2017}\hfill & \text{43}\hfill \\ \text{2010}\hfill & \text{33}\hfill & \hfill & \hfill \end{array}$