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Consider a distant AGN with a power law spectrum of energy slope 0.5
which is at a luminosity distance of 1000 Mpc and is viewed through
an absorption column of
cm 
(log(N 
).
The AGN luminosity in the ROSAT band is
L 
ergs s 
.
We want to determine how long an observation is required for a
detection.
The unabsorbed flux is
ergs cm 
s 
.
The ECF for this spectral model is taken from Table 11.3 or
Figure 11.5, it is 
,
which gives a count rate 
counts s 
.
Using the sensitivity formula from section 11.2,
we calculate that the observation time needed to detect this source
at the 
level (50% in detect cell) is about 12,600 seconds.