Question

Your shiny new boat cost $7650. The depreciation for your boat is 14% per year. You want to know the value of your vehicle in 3 years. What is the equation that models this problem?

Answer 1

The equation is

`V(3) = 7650(0.86)^(3)`

Which means that the value of the vehicle in 3 years is $4,865.8

Explanation:

The equation for the value of a product with a depreciation rate of r(as a decimal) is given by:

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

In which V(0) is the initial value.

Your shiny new boat cost $7650

This means that
`V(0) = 7650`

The depreciation for your boat is 14% per year.

This means that
`r = 0.14`

So

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

`V(t) = 7650(1-0.14)^(t)`

`V(t) = 7650(0.86)^(t)`

You want to know the value of your vehicle in 3 years. What is the equation that models this problem?

The equation is

`V(3) = 7650(0.86)^(3)`

Which means that the value of the vehicle in 3 years is $4,865.8