Answer
$\Delta t = 16~ps$
Work Step by Step
We can find the time $\Delta t$ that must elapse:
$P = r~\Delta t$
$P = (\frac{1}{\tau})~(\Delta t)$
$\Delta t = P~\tau$
$\Delta t = (0.01)~(1.6~ns)$
$\Delta t = 0.016~ns$
$\Delta t = 16~ps$
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