Your brand new 20,000 car will depreciate to 2,000 at a constant rate in ten years. Write a linear model relating the value "v" with the time since purchase "t".

Define

v = value after t years.

Therefore the linear model is

v = mt + c

where

m = depreciation rate

t = years since purchase

c = constant

When t=0, v = 20,000, therefore

20000 = m (0) + c

c = 20000

When t=10, v = 2000, therefore

2000 = 10m + 20000

-18000 = 10m

m = - 1800

Answer:

The linear model is

v = - 1800t + 20000

Given that the brand new car that cost 20000 depreciates at the rate v in 10 years, the linear model for the value, v will be given as follows:

The linear model follows a linear equation given by:

y=mx+c

where, m is the rate and c is the constant. From our equation:

c=20,000

m=2000

v (0) = 20000

v (10) = 2000

the slope will be:

m = (2000-20000) / (10-0) = - 1800

the equation will be:

v (t) = - 1800t+20000