9

Set 6: Exponential Functions (Advanced)

Explanation

Answer: A

A car depreciates at 15% per year. If purchased for $25,000, what is its value after 4 years?

A.

$13,050.06

✓ Correct
B.

$10,000

C.

$15,000

D.

$20,000

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Use exponential decay for depreciation. 1. Retention Rate: If it loses 15%, it keeps 85% = 0.85. 2. Formula: V(t)=25000(0.85)tV(t) = 25000(0.85)^t where t=4t = 4. 3. Calculate: V(4)=25000(0.85)4=25000(0.52200625)13,050.06V(4) = 25000(0.85)^4 = 25000(0.52200625) \approx 13,050.06. Strategic Tip: Depreciation of 15% means retention factor of 0.85. Choice B is incorrect because this assumes too much depreciation. Choice C is incorrect because this assumes only 1-2 years of depreciation. Choice D is incorrect because this assumes only 1 year of depreciation.

Key Steps:

The correct answer is $13,050.06

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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