Why is SVD curve not matching original data?

I am attempting to fit a curve with a sum of exponentials using SVD methods because it is more robust and utilize linear methods. My equation is y=Aexp(-bx) and so on. My coefficient matrix consists of a range of values and each column is the form exp(-f(1).\x)then using SVD to solve for A. However, when I perform the SVD curve fit the data does not match. I am wondering if my range of values are incorrect or my SVD method. I have attempted to debug the program but am having minimal luck

x=[1,2,4,6,8,10,15,20,35,50,75,100,150,200,350,500,1000,1750]' rates=(3:22.4:400); %rates 1/.002 to 1/.4

%Coefficent matix y1=exp(-rates(1).\x); y2=exp(-rates(2).\x); y3=exp(-rates(3).\x); y4=exp(-rates(4).\x); y5=exp(-rates(5).\x); y6=exp(-rates(6).\x); y7=exp(-rates(7).\x); y8=exp(-rates(8).\x); y9=exp(-rates(9).\x); y10=exp(-rates(10).\x); y11=exp(-rates(11).\x); y12=exp(-rates(12).\x); y13=exp(-rates(13).\x); y14=exp(-rates(14).\x); y15=exp(-rates(15).\x); y16=exp(-rates(16).\x); y17=exp(-rates(17).\x); y18=exp(-rates(18).\x);

R=[y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16,y17,y18];

%Known Y-Data C =-1035823.02839571 847374.054004519 3549764.66839471 6201540.15418506 9487905.85664665 11403261.1885086 14856766.4338426 17855334.2231497 21603166.0901448 23184839.8788382 23784630.1433765 23374945.0221579 21273930.1796291 19189277.0203142 13196478.7352441 9301576.70628163 3128301.20806591 1256379.88841090

 [U, S, V]=svd(R); %get svd
 Ut=transpose(U); %transpose U

P=V*S*U'; A=inv(P)*C;

y_SVD=R*A;

figure(1) hold on; semilogx(tmix,-y_SVD,'-r') semilogx(tmix,C,'-bl') hold off;