Help with plotting solution curves to the Gompertz equation

I'm relatively new in Mathematica. I already checked this post: Need code for differential equation analysis $\dot{x} = rx \ln \frac{K}{x}$ but it doesn't seems to help me. I apologize in advance if this kind of question was already asked, but I don't find an answer that can help me with the following issue: I'm solving the Gompertz equation:

$$\frac{dN}{dt}=-aN\ln(bN)$$

with initial conditions $N(0)=\frac{1}{2b}$

I want to plot the solution curves of this equation with the following conditions: \begin{aligned}-3\leq t\leq3\text{ et }-3\leq N\leq3.\end{aligned} all in one graph. something like this:

after trying using the function DNsolve in mathematica with no success, I decided I would plot directly from the solution of the equation: $$N(t)=\frac{1}{b}\exp({\ln{(1/2)}e^{-at}})$$

I use $a=2$ and $b=2$. I wrote the following code:

ClearAll["Global`*"] b = 2; cValue = Log[1/2]; (*cte d'integration*) a = 2; f[t_] = 1/b*Exp[cValue*Exp[-a*t]] curve1 = Plot[1/b*Exp[cValue*Exp[-a*t]], {t, -3, 3}, PlotStyle -> {Thickness[0.0065], Blue}, PlotRange -> All, PlotLabel -> "Plot pour condition N(0)", AxesLabel -> {"t", "N"}] (*plots pour plusieurs solutions pour les intervalles -3<t<3 et \ -3<n<3*) samples1 = table[f[t], {t, -3, 3, 1}]; curves = Plot[Evaluate[samples1], {t, -3, 3}, PlotStyle -> {Black}]; Show[curves, curve1] 

but I get this:

I can plot the curve with the initial condition (where the constant equals $\log(1/2)$) but not the other solution curves in the given interval. Can someone kindly help me to plot the family of curves or indicate me how can I do it with ND solve?

Thanks in advance