Question

A new 2006 Honda head was values at $25000. It depresides at a rate of 13% a year.

1. What was its value in 2009
2.What will be its value in 2020?

Answer 1

1. It's value in 2009 was $16,462.575

2. It's value in 2020 will be $3,558.

Explanation:

The equation for the value of car after t years has the following format.

`V(t) = V(0)(1-r)^(t)`

In which V(t) is the value after t years, V(0) is the initial value and r is the ratio of depreciation.

In this problem, we have that:

`V(0) = 25000, r = 0.13`

So

`V(t) = V(0)(1-r)^(t)`

`V(t) = 25000(1-0.13)^(t)`

`V(t) = 25000(0.87)^(t)`

1. What was its value in 2009

2009 is 3 years after 2006, so this is V(3)

`V(t) = 25000(0.87)^(t)`

`V(3) = 25000(0.87)^(3)`

`V(3) = 16462.575`

It's value in 2009 was $16,462.575

2.What will be its value in 2020?

2020 is 14 years after 2006, so this is V14)

`V(t) = 25000(0.87)^(t)`

`V(14) = 25000(0.87)^(14)`

`V(14) = 3558`

It's value in 2020 will be $3,558.