SOLUTION
It begins to depreciate at a rate of 18.9% annually. This means that the rate at which the value is decreasing is exponential. We would apply the formula for exponential decay which is expressed as
[tex]y=b(1-r)^t[/tex]
Where,
y represents the value of the car after t years.
t represents the number of years.
b represents the initial value of the car.
r represents the rate of depreciation.
Given
[tex]\begin{gathered} P=\text{ \$28000} \\ r=18.9\%=\frac{18.9}{100}=0.189 \\ \end{gathered}[/tex]
Therefore,
[tex]\begin{gathered} y=28000(1-0.189)^t \\ \therefore y=28000(0.811)^t \end{gathered}[/tex]
Where C(t) represents y,
Therefore, the function becomes
[tex]C(t)=28000(0.811)^t[/tex]
Hence, the function that describes the value of the car after t years is
[tex]C(t)=28000(0.811)^t\text{ (OPTION 1)}[/tex]
