Camper van depreciation — exponential model for a $38,000 van with 15% annual decline (y = 38000(0.85)^x)

Exponential equation modeling the value of a $38,000 camper van that depreciates 15% per year. Includes the equation y = 38000(0.85)^x and example values after 1 and 5 years.

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Identify the initial value and the yearly multiplier:

  1. Initial value a = $38,000 (the van's purchase price).
  2. Yearly depreciation rate = 15% → yearly multiplier b = 1 − 0.15 = 0.85.

So an exponential model in the form y = a(b)^x is:

y = 38000(0.85)x

Here x is the number of years, y is the van's value after x years. For example:

  • After 1 year: y = 38000(0.85) = $32,300.
  • After 5 years: y = 38000(0.85)5 ≈ $16,860.80.

Because b = 0.85 (between 0 and 1), the model represents exponential decay.

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