Respuesta :
From the depreciation formula:
[tex]A=P(1-\frac{r}{100})^n[/tex]we know the final value A=$11,000, the initial values P=$38000 and the number of years n=6. Then, we need to find the rate r. By substituting these values into the formula, we have
[tex]11000=38000(1-\frac{r}{100})^6[/tex]Then, by dividing both sides by 38000, we get
[tex]\begin{gathered} \frac{11000}{38000}=(1-\frac{r}{100})^6 \\ or\text{ equivalently,} \\ (1-\frac{r}{100})^6=0.28947 \end{gathered}[/tex]Now, by applying 6th root to both sides, we have
[tex](1-\frac{r}{100})=0.813332[/tex]by subtracting 1 to both sides, we have
[tex]-\frac{r}{100}=-0.186667[/tex]or equivalently,
[tex]\frac{r}{100}=0.186667[/tex]Then, the rate is given by
[tex]\begin{gathered} r=100\times0.186667 \\ r=18.6667\text{ \%} \end{gathered}[/tex]Once we know the rate, we can find the car's value by 2017. Then, we have
[tex]A=38000(1-\frac{18.667}{100})^{10}[/tex]where n=10 years (from 2007 to 2017). By computing the term into the paranthesis, we have
[tex]\begin{gathered} A=38000(1-0.18667)^{10} \\ A=38000(0.813332)^{10} \end{gathered}[/tex]which gives
[tex]\begin{gathered} A=38000(0.12667) \\ A=4813.549 \end{gathered}[/tex]Therefore, the answer is $4813.549
