Answer:
The approximate value of the car after 7 years is;
[tex]\text{ \$9,565.94}[/tex]Explanation:
Given that the initial value of the car is;
[tex]P=\text{ \$20,000}[/tex]after 1 year its new value is;
[tex]\text{ \$18,000}[/tex]The rate of depreciation is;
[tex]r=\frac{18000}{20000}=0.9\text{ per year}[/tex]After 7 years the value of the car can be calculated using the formula;
[tex]F=P(r)^t[/tex]where t equals 7 years.
substituting the values;
[tex]\begin{gathered} F=20000(0.9)^7 \\ F=\text{ \$9,565.94} \end{gathered}[/tex]Therefore, the approximate value of the car after 7 years is;
[tex]\text{ \$9,565.94}[/tex]