I agree with the judicious Reinderien's answer.

In order to confirm I tried a very different method which is not iterative and which doesn't need initial estimate. That way the lack of estimate or bad estimate doesn't affect the result.

The principle of the method with integral equation is explained in https://fr.scribd.com/doc/14674814/Regressions-et-equations-integrales

The algorithm is very simple :

For example with MathCad :

The fitted curve ( in red on the figures below ) is quite indistinguishable from the curve obtained by Reinderien.

Of course the found approximates a=74.9 ; b=728 ; c=-0.545 could be used as very good initial estimate for an usual iterative method of regression.