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A new fitness app has \(8,000\) subscribers at its launch. Each month, the data shows that \(10\pourcent\) of the existing subscribers cancel their subscription, but \(1,200\) new people sign up.
  1. Determine the number of subscribers after one month.
  2. Model the problem using a sequence \((u_n)\).
  3. Determine the expression of \(u_n\) in terms of \(n\).
  4. Determine the limit of the sequence \((u_n)\) and interpret it in the context of the problem.

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