Confidence interval for an inverse rate ($[{\lambda }_L,{\lambda }_U]\mapsto [1/{\lambda }_U,1/{\lambda }_L]$)

For an exponential distribution with positive rate $\lambda$, the mean is $1/\lambda$. A confidence interval for the rate transforms to one for the mean by reversing and inverting its endpoints. The monotonic transformation preserves the coverage event; it does not give a prediction interval for one realized holding time.