Question

Zachary purchased a new car for $21,995. The value of the car linearly depreciated to $9,100 over 10 years. Write a linear equation to represent the value y of Zachary's car (in dollars) after x years since its purchase.

Answer 1

y(x) = 21995 - 12895.5x

Explanation:

The value of the car after x years is given by the following linear function:

`y(x) = y(0) - ax`

In which y(0) is the initial value and a is how much it depreciates per year.

Zachary purchased a new car for $21,995. The value of the car linearly depreciated to $9,100 over 10 years.

This means that
`y(0) = 21995, y(10) = 9100`

So

`y(x) = 21995 - ax`

`9100 = 21995 - 10a`

`10a = 12895`

`a = (12895)/(10)`

`a = 12895.5`

So

y(x) = 21995 - 12895.5x