The latest version of the TestEDS utility can now also calculate predicted count rates using the exponential expression, here using 1.5 usec dead time constant:

Plotted up this looks like this:

As we can see, the exponential math fails at around 240K cps at 1.5 usec, so the calculation skips the application of a dead time correction above that point.

In fact, all the dead time expressions (including the traditional linear expression) fail at sufficiently high dead times and/or count rates, but even the logarithmic expression works up to an input (observed) count of ~420K cps (at 1.5 usec), which corresponds to a predicted count rate of ~2 * 10^8 cps!

PS: the TestEDS application is found in the Utilities menu in the Probe for EPMA menu under the Windows Start button. Try out some various dead time constants and see for yourself.