4
advanced-math

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

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

Correct Answer: A

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 0.880.88 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.