3

Set 7: Exponential Functions (Advanced)

Explanation

Answer: A

An antique increases in value by 12% per year. If currently worth $5,000, what will it be worth in 10 years?

A.

$15,529.24

✓ Correct
B.

$11,000.00

C.

$20,000.00

D.

$6,000.00

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Apply exponential appreciation. 1. Formula: V(t)=5000(1.12)tV(t) = 5000(1.12)^t where t=10t = 10. 2. Calculate: V(10)=5000(1.12)10=5000(3.10585)15,529.24V(10) = 5000(1.12)^{10} = 5000(3.10585) \approx 15,529.24. 3. Result: Value ≈ $15,529.24. Strategic Tip: 12% growth means multiplying by 1.12 each year. Choice B is incorrect because this assumes simple interest (5000 + 6000). Choice C is incorrect because this growth is too high. Choice D is incorrect because this is only 1 year of growth.

Key Steps:

The correct answer is $15,529.24

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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