In 2003, the price of a certain automobile was approximately $32,900 with a depreciation of $2,080 per year. After how many years will the car's value be $18,340?

Question

Write an equation to model the problem. Let t represent the number of years after 2003. For example, the year 2005 would be represented by t = 2.

I already have the number of years for part b, which is 11 years. I tried studying the answers others got provided with and applied them to my own, but I still couldn't seem to get the right answer no matter how much I tried.

Answer 1

Let V(t) be the value of the car t years after 2003.

So V(0)= 32900(= Value of car in 2003)

V(1) = 32900 - 2080 (= Value of car in 2004)

V(2) = V(1) - 2080= 32900 - 2080 - 2080

= 32900- (2•2080) (=Value of car in 2005)

V(t) = 32900 - (t •1840) =Value of car in 2003+t

where t=0,1,2,3,….15 (cos when t=16 value would be negative)

and so V(t)=0 if t >=16.

Equation you want to solve is

V(t)=32900-(t•2080)=18340

So, 32900-18340=t•2080, which implies,

14560=t•2080, and thus 14560/2080=7=t.

Thus the year is 2003+7=2010.

Unless your question has other missing information, the answer is 7 years after 2003.