Potassium-argon dating is accurate from 4.3 billion years (the age of the Earth) to about 100,000 years before the present. At 100,000 years, only 0.0053% of the potassium-40 in a rock would have decayed to argon-40, pushing the limits of present detection devices.

What will happen to a rock that contains potassium and argon after 1.3 billion years?

It has a half-life of 1.3 billion years, meaning that over a period of 1.3 Ga one-half of the 40K atoms in a mineral or rock will decay to 40Ar, and over the next 1.3 Ga one-half of the remaining atoms will decay, and so forth (Figure 19.18). Potassium feldspar does not contain any argon when it forms.