Question

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" .

Answer 1

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

Answer 2

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