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An initial capital of 1,200 dollars is invested at a compound annual interest rate of 2\(\pourcent\) on January 1, 2020.
We model the situation with a sequence \((u_n)\) where \(u_n\) represents the capital in the year \(2020 + n\).
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 years will the capital have tripled?
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