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In 2021, a forest contains \(20,000\) trees. Every year, the local forestry department cuts down \(5\pourcent\) of the existing trees for wood production, but replants \(3,000\) new trees.
Determine the number of trees in 2022.
Model the problem using a sequence \((u_n)\).
Determine the expression of \(u_n\) in terms of \(n\).
Determine the limit of the sequence \((u_n)\) and interpret it in the context of the problem.
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