Exponential Decay
The value of the car can be modeled with an exponential decay function:
[tex]V(t)=V_o\cdot(1-r)^t[/tex]
Where V(t) is the resale or residual value of the car after t years, Vo is the initial value (purchased price), and r is the decay rate.
The car was purchased for Vo = $26,000 and the price decays by r = 35% = 0.35 per year, thus our function is:
[tex]\begin{gathered} V(t)=26,000\cdot(1-0.35)^t \\ Operate\colon \\ V(t)=26,000\cdot(0.65)^t \end{gathered}[/tex]
The resale value after t = 4 years is:
[tex]\begin{gathered} V(4)=26,000\cdot(0.65)^4 \\ V(4)=26,000\cdot0.17850625 \\ V(4)=4,641 \end{gathered}[/tex]
The resale value is $4,641
