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Answered

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?

Verified Answer :

konrad509

y - value
x - year

\(24000=a\cdot3+b\\ 19000=a\cdot5+b\\\\ 24000=3a+b\\ -19000=-5a-b\\ ---------\\ 5000=-2a\\ a=-2500\\\\ b+3\cdot(-2500)=24000\\ b-7500=24000\\ b=31500\\\\ \boxed{y=-2500x+31500}\)

a)
\(f(x)=-2500x+31500\\ f(x+1)=-2500(x+1)+31500\\ f(x+1)=-2500x-2500+31500\\ f(x+1)=-2500x+29000\\\\ f(x)-f(x+1)=-2500x+31500-(-2500x+29000)\\ f(x)-f(x+1)=-2500x+31500+2500x-29000\\ f(x)-f(x+1)=\boxed{2500}\)

b)
\(f(0)=-2500\cdot0+31500=\boxed{31500}\)

c)
\(f(10)=-2500\cdot10+31500\\ f(10)=-25000+31500\\ f(10)=\boxed{6500}\)

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