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" .

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