How many searchers to hire for a lost drive

Gabe has lost a USB drive holding $\text{\char36}500{,}000$ in Bitcoin, and the money is gone for good unless the drive turns up within a week. He can hire searchers at $\text{\char36}5{,}000$ each for the week, and each searcher independently has a $90\%$ chance of finding it. How many searchers maximise his expected outcome?

$2$. In units of $\text{\char36}5{,}000$, hiring $n$ searchers yields expected value $100\left(1-0.1^n\right)-n$, i.e. we minimise $100\cdot0.1^n+n$. This is $11$ for $n=1$, $3$ for $n=2$, and at least $3.1$ for $n\ge3$.