100 billion (approximately). If a samarium sample was created at the beginning of Earth's history, that would put it at the same age as earth (4.6 billion years). If samarium's half life is 106 billion years, and 4.6 billion years have already passed, then 106 billion - 4.6 billion leaves you with 101.4 billion years left till it's half life (rounds closest to 100 billion years from answer choices).