clear
format long

% input intial data
S=[.01 .05 .1 .5 1 5 10 50 100];
v0= [6.078e-11 7.595e-9 6.063e-8 5.788e-6 1.737e-5 2.423e-5 2.43e-5 2.431e-5 2.431e-5];

% if our model is valid, a plot of 1/v0 versus 1/S^3 should yield a
% straight line with a slope of K/km and an intercept of 1/km. The slope
% and intercept can be implemented in MATALB using linregr.m 
a=linregr(1./S.^3, 1./v0)

% we can use these results to compute k_m & K
km= 1/a(2)
K=km*a(1)

% Now we have our best fit model v0
v0p= km*S.^3./(K+S.^3);
% To handle the wide variation of the magnitudes of the displayed values,
% use loglog plot
loglog(S,v0,'o', S, v0p)