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In a culture medium, at time \(t=0\), we observe the presence of 10,000 bacteria. This number is multiplied by 1.5 every hour. We model the situation using a sequence \((u_n)_{n \in \mathbb{N}}\), where \(u_n\) represents the number of bacteria present \(n\) hours after the first observation.
Show that \((u_n)\) is a geometric sequence. Specify its first term \(u_0\) and its common ratio \(q\).
Express \(u_n\) in terms of \(n\).
After how many hours will the number of bacteria exceed one million?
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