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

3400

Explanation:

y=a(1/2)^t/h

a=36000 h=5 t=17

plug in

Answer 2

$3400

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.