A new car cost 28000 After 3 years its value is 16000 The de

A new car cost $28,000. After 3 years its value is $16,000. The depreciation of the car is assumed to be linear.

a. Find an equation that expresses the value of the car in terms of the age

b. What is the value of the car after 5 years ?

c. When will the car have no value ?

Solution

Cost = $ 28000

After 3 years its value is $16,000

So relation is linear it can be modelled by a straight line equation: y = mx +c where

x is the no. of years and y is the cost of car.

slope = ( 16000-28000)/3

= -4000

Find y intercept : y = -4000x +c ----> c= 28000

a) So, y = -4000x + 28000

b) Value of car after 5 years: y = -4000*5 + 28000 = $ 8000

c) No value : y=0 so, 0=-4000x + 28000

x = 28000/4000 = 7 years . In 7years car has 0 value