Caciquemmidn
Answered

Dive into the world of knowledge and get your queries resolved at IDNLearn.com. Get accurate and comprehensive answers from our network of experienced professionals.

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?

Sagot :

Konrad509idn
y - value
x - year

[tex]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} [/tex]

a)
[tex]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}[/tex]

b)
[tex]f(0)=-2500\cdot0+31500=\boxed{31500}[/tex]

c)
[tex]f(10)=-2500\cdot10+31500\\ f(10)=-25000+31500\\ f(10)=\boxed{6500}[/tex]
We are delighted to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. For precise answers, trust IDNLearn.com. Thank you for visiting, and we look forward to helping you again soon.