Why are the estimated coefficients returned by NLINFIT all the same?

I am performing a nonlinear regression to determine the best fit coefficients for a t^1/2 plot that becomes linear after a certain time (x). I want to find the best estimate for time.

When I input my initial guesses into nlinfit, nlinfit returns coefficients which are all the same. I cannot figure out why. I would ideally like to have a unique estimate for all my initial guesses so I can find the minimum misfit coefficient. Having non-unique estimates prevents me from doing this.

Help?

t_t     = [75:0.5:85];        % Ma -- Age at which slop switches
m1      = 300;                % m/Ma -- slope before t-t
m2      = 0.825;              % 0.825 (best by forward model) m/Ma -- slope after t-t
b1      = 3000;               % m -- y-intercept before t-t

% Anonymous function

test_fcn = @ (coef,t) (coef(2)*sqrt(t) + coef(3)).*(t <= coef(1)) + ( coef(4) *(t) + (m1*sqrt(coef(1)) + b1)).*(t > coef(1));

M = zeros(length(t_t),9);

for i = 1:length(t_t);
    % Make matrix of guesses
        guess = [t_t(i) m1 b1 m2]

      % Run nlinfit
          fit = nlinfit(age,depth,test_fcn, guess);

      % Store fit values in matrix
          sfit = [fit(1) fit(2) fit(3) fit(4)];

      % Calculate yfit using anonymous function
          depth_fit = test_fcn(sfit,age);

      % Calculate the goodness of fit for these parameters
          misfit = sum((abs(depth - depth_fit)).^2);

      % Store everything in a matrix
          M(i,1:9) = [guess(1:4) sfit(1:4) misfit(1)];

end

    My initial guesses:
    75
    75.5
    76
    76.5
    77
    77.5
    78
    78.5
    79
    79.5
    80
    80.5
    81
    81.5
    82
    82.5
    83
    83.5
    84
    84.5
    85

    NLINFIT estimated Coefficients
    73.8342585833035
    73.8342585765359
    79.9997047357170
    79.9995763838739
    79.9995991045945
    79.9995531864376
    79.9995871290049
    79.9997041272140
    79.9995740570344
    79.9996143251319
    79.9995155307410
    79.9996903874223
    79.9996050266437
    79.9995910209715
    79.9995429091664
    79.9995538921889
    79.9995486637682
    79.9995813685956
    79.9995991398304
    79.9995677153829
    79.9996795763662

[the cyclist]

Unless I missed something, we can't run your code because we do not have the age and depth variables defined.