The table shows the numbers (in thousands) of alternative-fueled vehicles A in use in the United States from 1995 to 2011. (Source: U.S. Energy Information Administration) Year Number of vehicles, A 1995 246.9

1996 265.0

1997 280.2

1998 295.0

1999 322.3

2000 394.7

2001 425.5

2002 471.1

2003 534.0

2004 565.5

2005 592.1

2006 634.6

2007 695.8

2008 775.7

2009 826.3

2010 838.6

2011 1191.8

(a) Use a graphing utility to plot the data. Let t represent the year, with t = 5 corresponding to 1995. (b) A model for the data is A=4615.36t8726.7/1+15.01t0.542t2,5t21 where t = 5 corresponds to 1995. Use the model to estimate the numbers of alternative-fueled vehicles in 1996, 2006, and 2011. How do your answers compare to the original data? (c) Use a graphing utility to graph the function with the original data. (d) Find the limit of the function as t approaches infinity. (e) Interpret your answer from part (d) in the context of the problem. Does your answer make sense? Explain your reasoning. (f) Use the model to predict the numbers of alternative-fueled vehicles in 2016 and 2017. (g) Do you think this model could be used to predict the numbers of alternative-fueled vehicles for future years? Explain your reasoning. Project: Alternative-Fueled Vehicles