6

Set 12: Exponential Functions

Explanation

Answer: A

A new phone loses 30% of its value each year. If it costs $1,200 new, what will it be worth after 3 years?

A.

$411.60

✓ Correct
B.

$360.00

C.

$840.00

D.

$600.00

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Apply depreciation formula. 1. Retention: Loses 30%, keeps 70% = 0.70. 2. Formula: V(t)=1200(0.70)tV(t) = 1200(0.70)^t where t=3t = 3. 3. Calculate: V(3)=1200(0.70)3=1200(0.343)=411.60V(3) = 1200(0.70)^3 = 1200(0.343) = 411.60. Strategic Tip: Loses 30% means retention factor of 0.70. Choice B is incorrect because this assumes 70% loss, not retention. Choice C is incorrect because this is the value after 1 year. Choice D is incorrect because this is the value after a 50% loss total.

Key Steps:

The correct answer is $411.60

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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