Problema Solution
Three years after purchase, a car is estimated to be worth $24,000. At five years, its value is $19,000. If the car is depreciating in a linear manner, write an equation that represents the depreciation of the car. Answer the following questions:
a. How much is the car depreciating each year?
b. What was the purchase price of the car?
c. If the car continues this rate of depreciation, what will its value be at year 10?
Answer provided by our tutors
When it was bought new, the time was x = 0 years and the value was p the purchase price.
after x = 3 years the car is estimated to be worth y = $24,000
after x = 5 years the car is estimated to be worth y= $19,000
This amounts to finding the equation of a line that passes through the two points (3, 24000) and (5, 19000), where x represents the time and y represents the value of the car.
m = (y2 - y1)/(x2 - x1)
where (x1,y1) = (3, 24000) and (x2,y2) = (5, 19000)
m = (19000 - 24000)/(5 - 3)
m = -2500
Now use the point-slope formula:
y - y1 = m(x - x1)
y - 24000 = -2500 (x - 3)
y = -2500x + 31,500
a. each year the car is depreciated by $2,500
b. we get the purchase price of the car for x = 0 that is:
y = -2500*0 + 31,500
y = $31,500
the purchase price of the car was $31,500.
c. after 10 years means x = 10
y = -2500*10 + 31,500
y = $6,500
after 10 years the value of the car will be $6,500.