Question

A new car is purchased for $36,000 and over time its value depreciates by
one half every 5 years. What is the value of the car 17 years after it was
purchased, to the nearest hundred dollars?

Answer 1

Answer:

  $3400

Step-by-step explanation:

The exponential function describing the value can be written as ...

  v(t) = (initial value) · (growth factor)^(t/(growth period))

You are given ...

  initial value = 36000

  growth factor = 1/2

  growth period = 5 years

Then the function is ...

  v(t) = 36000(1/2)^(t/5) . . . . where t is in years

For t = 17, the value is ...

  v(17) = 36000 · (1/2)^(17/5) ≈ 3410.36

17 years after it was purchased, the value is predicted to be about $3400.