Respuesta :
Given the initial value of the car at $22,000 and the annual depreciation value at 35%. To calculate the resale value of the car after a given number of years, we shall apply the exponential decay formula;
[tex]f(x)=a(1-r)^x[/tex]This can also be written as;
[tex]y=a(1-r)^t[/tex]The value of x in the first equation is the same as the value of t in the second equation. x is the number of years, and t is also the same, the number of years.
Therefore, with the values already given, we would have;
[tex]\begin{gathered} \text{Where;} \\ a=\text{initial value}=22000 \\ r=\text{rate of depreciation}=0.35\text{ (35\%)} \\ t=\text{time in years}=4 \end{gathered}[/tex]The resale value after 4 years would now be;
[tex]\begin{gathered} y=a(1-r)^t \\ y=22000(1-0.35)^4 \\ y=22000(0.65)^4 \\ y=3927.1375 \\ \text{Rounded to the nearest dollar;} \\ y=3,927 \end{gathered}[/tex]ANSWER:
The resale value after 4 years would be $3,927
