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A new car is purchased for \$14,000$14,000 and over time its value depreciates by one half every 5.5 years. What is the value of the car 18 years after it was purchased, to the nearest hundred dollars



Answer :

sqdancefan

Answer:

  $1400

Step-by-step explanation:

You want the value of a car 18 years on if its initial value was $14,000 and its value is cut in half every 5.5 years.

Exponential model

The value of the car can be modeled by the exponential equation ...

  value = (initial value) × (growth factor)^(t/(growth period))

where "growth period" is the period applicable to the "growth factor."

Application

Here, the problem statement tells us ...

  • initial value = $14,000
  • growth factor = 1/2
  • growth period = 5.5 years

So, our exponential model is ...

  value = 14,000·(1/2)^(t/5.5)

When t=18 years, this is ...

  value = 14,000(1/2)^(18/5.5) = 14000(1/2)^(36/11) ≈ 14000·0.103469 ≈ 1449

The value after 18 years is about $1400.

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