8

Set 4: Exponential Functions

Explanation

Answer: A

A car's value follows V(t)=35000(0.88)tV(t) = 35000(0.88)^t where tt is years. What does 0.88 represent?

A.

The car retains 88% of its value each year

✓ Correct
B.

The car loses 88% of its value each year

C.

The initial price is $88,000

D.

The car gains 12% value each year

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Interpret the decay factor. 1. Form: V(t)=a(b)tV(t) = a(b)^t where b=0.88b = 0.88. 2. Meaning: Each year, value becomes 0.8888 times the previous year. 3. Retention: Keeps 88%, loses 12%. Strategic Tip: Decay factor of 0.88 means retaining 88%, not losing 88%. Choice B is incorrect because it misinterprets the factor (keeps 88%, not loses). Choice C is incorrect because 35,000 is the initial price. Choice D is incorrect because the car is depreciating, not appreciating.

Key Steps:

The correct answer is The car retains 88% of its value each year

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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