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:
[tex]C(t)=C_o\cdot(1-r)^t[/tex]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:
[tex]C(10)=17900\cdot(1-0.1225)^{10}[/tex]Calculating:
[tex]C(10)=17900\cdot0.2707\text{ = }4845.34[/tex]The value of the car will be $4845.34
