Question

A new toyota rav4 costs $23,500. the car's value depreciates linearly to $18,823 in three years time.1 write a formula which expresses its value, v, in terms of its age, t, in years.

Answer 1

For this case we must find a linear equation of the form:

$v = mt + b$

Where,

b: initial value of the car

m: decrease rate per year

t: number of years

v: value of the car

For the slope of the line we have:

$m = \frac{v2-v1}{t2-t1}$

$m = \frac{18823-23500}{3-0}$

$m = \frac{-4677}{3}$

$m = -1559$

The initial value of the car is:

$b = 23500$

So, replacing values we have:

$v = -1559t + 23500$

Answer:

a formula which expresses its value, v, in terms of its age, t, in years is:

$v = -1559t + 23500$