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A car depreciates 15% a year. What is a $24,000 car worth after 2 years?

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Answer
\boxed{17,340}

Checking the result, a 15% drop the first year leaves $20,400, and a 15% drop on that amount in the second year brings the value to $17,340.

Problem: Find the value of a $24,000 car after 2 years if it depreciates at a rate of 15% per year.

Steps

  1. Set up the exponential decay formula
    V=24000(1−0.15)2V = 24000(1 - 0.15)^2
  2. Simplify inside the parentheses
    V=24000(0.85)2V = 24000(0.85)^2
  3. Evaluate the exponent
    V=24000(0.7225)V = 24000(0.7225)
  4. Multiply to find the final value
    V=17340V = 17340

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