7

Set 6: Exponential Functions

Explanation

Answer: A

A vehicle depreciates 22% per year. If bought for $35,000, what's its value after 5 years?

A.

$10,404.67

✓ Correct
B.

$15,000.00

C.

$20,000.00

D.

$12,500.00

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Apply depreciation formula. 1. Retention: Loses 22%, keeps 78% = 0.78 each year. 2. Formula: V(t)=35000(0.78)tV(t) = 35000(0.78)^t where t=5t = 5. 3. Calculate: V(5)=35000(0.78)5=35000(0.2973)10,405V(5) = 35000(0.78)^5 = 35000(0.2973) \approx 10,405. Strategic Tip: High depreciation rates lead to rapid value loss. Choice B is incorrect because this underestimates the depreciation. Choice C is incorrect because this assumes much slower depreciation. Choice D is incorrect because the calculation is wrong.

Key Steps:

The correct answer is $10,404.67

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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