Solution
= Solution
For an <exponential distribution>, the <survival function> at the <median> equals one half. Thus $e^{-10\delta}=1/2$, and
$$
\boxed{\delta=\frac{\ln2}{10}\approx0.0693147\ \text{day}^{-1}}.
$$
The corresponding mean care time is $1/\delta=10/\ln2\approx14.43$ days; a ten-day <median> should not be substituted as the mean.