The reason Iam fittinf exponential to a known function is because this is how people are measuring the system that I am looking at, and to know the values range of the parameters I use to describe this system (x, y, z), I must fit it this way.

Would it be feasible for you to test each of these (by restarting Mathematica each time and then doing a trivial calculation to start up the kernel and then using AbsoluteTiming) to see how much, if any, time each of these might save versus how much your graph is degraded?

Try substituting {t, 0, 25000, 100} or some other larger number for {t, 0, 25000, 10}

Try removing N[..., 15] to use perhaps faster machine precision calculations

Try removing WorkingPrecision->10 for the same reason

Try changing PlotPoints->10 to PlotPoints->20

The idea is to find which of those or which combination of those might give you enough increase in speed and still have satisfactory graphics resolution.

Are there missing _ between x? and between y? in your code or not? Those are different from your z_? Is there a comma missing in your code, perhaps because you had a newline between your two equations and when that was pasted that was lost?