A rock containing potassium-40, a radioisotope with a half-life of 1.30 billion years. Potassium-40 has a 89% chance to decay into Calcium-40 and a 11% chance to decay into Argon-40. Assuming that Argon-40 is stable and stays in the rock. There is no Argon-40 in the rock today. The only source of Argon-40 is from the decay of Potassium-40. Calculate what the ratio of will be 3.90 billion years from now.
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