data = [0 5.8955;
0.1000 3.5639;
0.2000 2.5173;
0.3000 1.9790;
0.4000 1.8990;
0.5000 1.3938;
0.6000 1.1359;
0.7000 1.0096;
0.8000 1.0343;
0.9000 0.8435;
1.0000 0.6856;
1.1000 0.6100;
1.2000 0.5392;
1.3000 0.3946;
1.4000 0.3903;
1.5000 0.5474;
1.6000 0.3459;
1.7000 0.1370;
1.8000 0.2211;
1.9000 0.1704;
2.0000 0.2636];

%init_theta = [0 0 0 0];  
%theta = fminsearch('fun_e1', init_theta, [], data);    
%x = data(:, 1);    
%y = data(:, 2);     
%estimated_y = theta(1)*exp(theta(3)*x)+theta(2)*exp(theta(4)*x);  
%plot(x, y, 'ro', x, estimated_y, 'b-');  
%legend('Sample data', 'Regression curve');    

init_lambda = [0 0];  
lambda = fminsearch('fun_e2', init_lambda, [], data);  
x = data(:, 1);  
y = data(:, 2);  
A = [exp(lambda(1)*x) exp(lambda(2)*x)];  
a = A\y;  
estimated_y = a(1)*exp(lambda(1)*x)+a(2)*exp(lambda(2)*x);  
plot(x, y, 'ro', x, estimated_y, 'b-');  
legend('Sample data', 'Regression curve');