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The value of a high-end laptop computer depreciates exponentially over time. Its value \(V(t)\) (in dollars) \(t\) years after purchase is modelled by \(V(t) = A e^{kt}\).
  • The laptop was purchased new for \(\dollar\)2000.
  • After 2 years, its value had dropped to \(\dollar\)1200.
  1. Identify the initial value parameter \(A\).
  2. Use the value at \(t=2\) to calculate the rate parameter \(k\) (round to 3 decimal places).
  3. Write the specific equation for the model.
  4. Estimate the value of the laptop after 5 years.

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