The Fifty-Fifty Crash Time

The gap between consecutive crashes of a server is exponentially distributed with rate $\lambda$ per day, so

$P(X > x) = e^{-\lambda x}, \qquad F(x) = P(X \le x) = 1 - e^{-\lambda x}$

Years of logs show that 40% of the gaps last longer than 30 days.

Find the time $m$, in days, at which there is exactly a 50% chance that the next crash has already happened. That is, find $m$ with $F(m) = 0.5$.

You may use $\ln(2) \approx 0.69315$ and $\ln(2.5) \approx 0.91629$.

Round to one decimal place.