Question

2. The population of the world for selected years from 1750 to 2009 is given in the following table: Year Population (millions) 1750 791 1800 980 1850 1,260 1900 1.650 1950 2,520 1990 5,270 2000 6,060 2009 6,800 (a) Determine the exponential function that best fits the data. Use the function to estimate the population in 1980. Make a plot of the points and the function. (b) Curve-fit the data with a third-order polynomial. Use the polynomial to estimate the population in 1980. Make a plot of the points and the polynomial. (©) Fit the data with linear and spline interpolations. Estimate the population in 1975 with linear and spline interpolations. Make a plot of the data points and curves made of the interpolated points. In each part make a plot of the data points (circle markers) and the fit curve or the interpolation curves. Note that part (c) has two interpolation curves. The actual population of the world in 1980 was 4453.8 million.

I want -C parts- using matlab

Answer 1

Please find the required MATLAB script for part (C) :

%==================================================================================

clear all;clc;format short

x = [1750,1800,1850,1900,1950,1990,2000,2009];
y = [791,980,1260,1650,2520,5270,6060,6800];

% Linear fit
p = polyfit(x,y,1); % Order 1 polynomial is essentially a line
y_lin_fit = polyval(p,x);
lin_1975 = polyval(p,1975);

% spline fit
y_spline_fit = interp1(x,y,x,'spline');
spline_1975 = interp1(x,y,1975,'spline');

fprintf('Population in 1975:\n1) by Linear fit: %f million, 2) by Spline fit: %f million\n',lin_1975,spline_1975);

figure
scatter(x,y)
hold on
plot(x,y_lin_fit,'-r')
hold on
plot(x,y_spline_fit,'--g')
legend('Original Data','Linear fit','Spline fit')
grid on
xlabel('Year')
ylabel('Population (million)')

%================================================================================

Output:

Population in 1975:
1) by Linear fit: 4717.218881 million, 2) by Spline fit: 4098.602853 million

7000 O Original Data Linear fit -Spline fit 6000 5000 4000 Population (million) 3000 2000 1000 0 -1000 1750 1800 1850 1950 2000 2050 1900 Year

In case of any clarification required, please comment!

******** PLEASE THUMBS UP!!!!!!! ********