Fitting solution function of NDSolve with a curve

[joshmccraney]

The following solves an IVP, giving the output as the function f3[x]:

s3 = NDSolve[{(-z1[t]^(3/2) + (1 + z1[t]^2)^(3/4))/(
    3 (-z1[t] + Sqrt[1 + z1[t]^2])) == z1[t] z1'[t], z1[0] == 0.0001},
   z1, {t, 0, 30}

f3[x_] := z1[x] /. First[s3];

My question is, how do I curve fit f3[x] to the function $at^b$ over domain $t\in[0,1]$? Looks like $t^{0.6}$ does a good job (by eye) but is there a better way?

 

[joshmccraney]

Nevermind, the solution is here: https://reference.wolfram.com/language/ref/FindFit.html which gives: $0.96556 t^{0.573358}$

FYI for future people I used

Table[f3[x], {x, 0, 1, 0.01}];
FindFit[%, a x^b, {a, b}, x]

and then used the $a,b$ output as $a(100t)^b$ where I used 100 since I incremented by 0.01, or 1/100.