Question

Alternative-Fueled Vehicles 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 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011	246.9 265.0 280.2 295.0 322.3 394.7 425.5 471.1 534.0 565.5 592.1 634.6 695.8 775.7 826.3 938.6 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

4615.36t − 8726.7

1 + 15.01t − 0.542t2, 5 ≤ t ≤ 21

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?

(f ) Use the model to predict the numbers of alternative-fueled vehicles in 2016 and 2017

* Need help to understand F . Should I be using a particular formula

Answer 1

%%Matlab code for plotting
clear all
close all

%data for year wise number of vehicles
year=[1995:2011];
A=[246.9 265 280.2 295 322.3 394.7 425.5 471.1 534 565.5 592.1 634.6 695.8 775.7 826.3 938.6 1191.8];

tt=5:21;

%2nd order polynomial fit
P=polyfit(tt,A,2);
f1=@(t) P(1).*t.^2+P(2).*t+P(3);

fprintf('function for 2nd order fit= (%2.2f)*t^2+(%2.2f)*t+(%2.2f) \n',P(1),P(2),P(3))

%3rd order polynomial fit
P=polyfit(tt,A,3);
f2=@(t) P(1).*t.^3+P(2).*t.^2+P(3).*t+P(4);

fprintf('function for 3rd order fit= (%2.2f)*t^3+(%2.2f)*t^2+(%2.2f)*t+(%2.2f) \n',P(1),P(2),P(3),P(4))

%1st model data
A1=f1(tt);

%2nd model data
A2=f2(tt);

hold on
plot(tt,A,'r*','linewidth',2);
plot(tt,A1)
plot(tt,A2)

xlabel('year')
ylabel('number of vehicle')
title('vehicle number vs. year plot')
legend('Actual data','2nd order fit','3rd order fit','location','best')

fprintf('\t the numbers of alternative-fueled vehicles in 2016 using 2nd order fit=%f\n',f1(26))

fprintf('\t the numbers of alternative-fueled vehicles in 2016 using 3rd order fit=%f\n',f2(26))

fprintf('\t the numbers of alternative-fueled vehicles in 2017 using 2nd order fit=%f\n',f1(27))

fprintf('\t the numbers of alternative-fueled vehicles in 2017 using 3rd order fit=%f\n',f2(27))

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