Question 1194480: A business owner decides to buy a company car for $53400 and assumes it will have a trade-in value of $21900 after 10 years. The business person uses a constant rate of depreciation (commonly called straight-line depreciation, one of several methods permitted by the IRS) to determine the annual value of the car.
(a) Find a linear model for the depreciated value V of the car t years after it was purchased?
V=
(b) What is the depreciated value of the car after 4 years?
dollars
(c) When will the depreciated value fall below $31700? Give an exact answer.
years
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! year, price
(0, 53400) and (10, 21900)
from those ordered pairs the slope is -315.
point-slope formula y-y1=m(x-x1), y slope and (x1, y1) point
y-53400=-3150(x)
or y=-3150x+53400
after 4 years, x=4 so y=-3150(4)+53400=$40,800
-
31700=-3150x+53400
so -3150x=-21700
x=6.89 years but exact is 434/63=62/9 years
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