Question

a car is purchased for 26,000 after each year the resale decrease by 35% what will the resale value be after 4 years ?

Answer 1

Exponential Decay

The value of the car can be modeled with an exponential decay function:

`V(t)=V_o\cdot(1-r)^t`

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:

`\begin{gathered} V(t)=26,000\cdot(1-0.35)^t \\ Operate\colon \\ V(t)=26,000\cdot(0.65)^t \end{gathered}`

The resale value after t = 4 years is:

`\begin{gathered} V(4)=26,000\cdot(0.65)^4 \\ V(4)=26,000\cdot0.17850625 \\ V(4)=4,641 \end{gathered}`

The resale value is $4,641