I have a function that looks like a sigmoid curve.
I would like to calculate the right integration border with which the area under the sigmoid curve amounts to a certain value.

my curve:

    model=(3.70288 E^(-((0.134844 (30.8 - 17.8731 t)^2)/t)))/Sqrt[t]

I tried:

    Solve[Integrate[model == 10^-2, {t, 0, x}], x]

But that didn't work.
Thanks in advance.