## Precalculus (6th Edition) Blitzer

$48$ years old.
Let $P(x)=50$; we have $\frac{90}{1+271e^{-0.122x}}=50$ and $271e^{-0.122x}=\frac{90}{50}-1=0.8$ Thus $x=-\frac{ln(0.8/271)}{0.122}\approx48$ years old.