Question

A new car is purchased for $18,000 and over time its value depreciates by one halfevery 6 years. What is the value of the car 19 years after it was purchased, to thenearest hundred dollars?

Answer 1

Answer: 2000

Explanation:

the answer is 2000 after rounding up 1999.9

Answer 2

We have the following:

We must pass the time from 19 years to periods of 6 years, as follows

`(19)/(6)=3.17`

That is, 19 years are 3.17 periods of 6 years

now, the formula to calculate the value of the car is

`c=A\cdot(1-x)^n`

Where A is the initial value, x is the depreciation and n is the time in periods of 6 years

Replacing:

`c=18000\cdot(1-0.5)^(3.17)=1999.89`

Therefore the value of the car would be approximately 1999.9 dollars