= Strong Hill autorepression response
{title2=$Y=Y_{\rm st}[1-e^{-(n+1)\alpha t}]^{1/(n+1)}$}
Neglecting the one in a strongly repressed <Hill equation> gives $\dot Y=\beta K^nY^{-n}-\alpha Y$. The substitution $z=Y^{n+1}$ makes this a linear <ordinary differential equation>. It yields $Y_{\rm st}=(\beta K^n/\alpha)^{1/(n+1)}$ and half-response time $-\log(1-2^{-(n+1)})/[(n+1)\alpha]$. The singular initial slope is an artifact of the approximation, whose range is not uniform at arbitrarily large $n$ and fixed production/degradation ratio.
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