10
advanced-math

A car's value depreciates exponentially. The table shows its value over three years. What is the annual depreciation rate?

YearValue ($)
030,000
124,000
219,200
A

20%

B

80%

C

24%

D

6%

Correct Answer: A

Choice A is the correct answer. Find the decay factor and convert to a rate.

  1. Decay Factor: b=24,00030,000=0.8b = \frac{24,000}{30,000} = 0.8.
  2. Verify: 19,20024,000=0.8\frac{19,200}{24,000} = 0.8 (consistent).
  3. Depreciation Rate: r=1b=10.8=0.2=20%r = 1 - b = 1 - 0.8 = 0.2 = 20\%.

💡 Strategic Tip: Depreciation rate = 1(decay factor)1 - \text{(decay factor)}. If the value keeps 80%, it loses 20%.

Choice B is incorrect because 80% is the retention rate (what remains), not the depreciation rate. Choice C is incorrect because this is the dollar amount lost in year 1, not the percentage rate. Choice D is incorrect because this doesn't match the pattern in the table.