Question

A new car is purchased for 17900 dollars. The value of the car depreciates at12.25% per year. What will the value of the car be, to the nearest cent, after 10years?

Answer 1

Exponential decay

The exponential function is widely used to model situations where the initial quantity of a given magnitude continuously loses value.

The mathematical model for depreciation is:

`C(t)=C_o\cdot(1-r)^t`

Where C(t) is the value of the car at any time t, Co is the initial value of the car, and r is the rate of decay.

The car was purchased for Co = $17900 and it depreciates at r=12.25% per year. The value of r must be expressed in decimal, thus r = 0.1225.

We are required to calculate the value of the car after t=10 years.

Substituting:

`C(10)=17900\cdot(1-0.1225)^(10)`

Calculating:

`C(10)=17900\cdot0.2707\text{ = }4845.34`

The value of the car will be $4845.34