04:41

Algebra and Trigonometry Real Mathematics, Real People

The populations $P$ (in thousands) of Luxembourg for the years 1999 through 2013 are shown in the table, where $t$ represents the year, with $t=9$ corresponding to 1999. (Source: European Commission Eurostat)

$$\begin{array}{|c|c|}\hline \text { Year } & \text { Population, } P \\\hline 1999 & 427.4 \\2000 & 433.6 \\2001 & 439.0 \\2002 & 444.1 \\2003 & 448.3 \\2004 & 455.0 \\2005 & 461.2 \\2006 & 469.1 \\2007 & 476.2 \\2008 & 483.8 \\2009 & 493.5 \\2010 & 502.1 \\2011 & 511.8 \\2012 & 524.9 \\2013 & 537.0 \\\hline\end{array}$$

(a) Use the regression feature of a graphing utility to find a linear model for the data and to identify the coefficient of determination. Plot the model and the data in the same viewing window.

(b) Use the regression feature of the graphing utility to find a power model for the data and to identify the coefficient of determination. Plot the model and the data in the same viewing window.

(c) Use the regression feature of the graphing utility to find an exponential model for the data and to identify the coefficient of determination. Plot the model and the data in the same viewing window.

(d) Use the regression feature of the graphing utility to find a logarithmic model for the data and to identify the coefficient of determination. Plot the model and the data in the same viewing window.

(e) Which model is the best fit for the data? Explain.

(f) Use each model to predict the populations of Luxembourg for the years 2014 through 2018.

(g) Which model is the best choice for predicting the future population of Luxembourg? Explain.

(h) Were your choices of models the same for parts

(e) and $(g) ?$ If not, explain why your choices were different.