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//Eg-10.5
//pg-437
clear
clc
close()
X = [0;5;10;15];
Y = [53;127;213;378];
T = zeros(4,4);
T(:,1) = Y;
for(j = 2:4)
for(i = 1:4+1-j)
T(i,j) = T(i+1,j-1) - T(i,j-1);
end
end
//disp(T)
// Using Gauss backward formula
//p3 = f + d*A + d2*A(A+1)/2 + d3*A*(A-1)*(A+1)/6
//Note that 'alpha' is replaced by A and 'small delta' by d
f = T(3,1);
d = T(2,2);
d2 = T(2,3);
d3 = T(1,4);
A = (7-10)/5;
p37 = f + d*A + d2*A*(A+1)/2 + d3*A*(A-1)*(A+1)/6;
printf('Therefore, the number of houses after seven years is %d\n',p37)
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