Answer:
The function f(x) representing the value of car after x years is given by
[tex]f(x)=\$ 20,000\times (1-\frac{15}{100})^{x}[/tex]
Step-by-step explanation:
Since value of car depreciates by 15% each year
Value of car after 1 year
[tex]f(1)=value of new car \times(1-\frac{15}{100})[/tex]
=>[tex]f(1)=\$ 20,000\times(1-\frac{15}{100})[/tex]
Value of car after 2 year
[tex]f(2)=\$ 20,000\times(1-\frac{15}{100})\times(1-\frac{15}{100})[/tex]
=>[tex]f(2)=\$ 20,000\times(1-\frac{15}{100})^{2}[/tex]
Value of car after 3 year
[tex]f(3)=\$ 20,000\times(1-\frac{15}{100})\times(1-\frac{15}{100})\times(1-\frac{15}{100})[/tex]
=>[tex]f(3)=\$ 20,000\times(1-\frac{15}{100})^{3}[/tex]
Similarly value of car after x years is
[tex]f(x)=\$ 20,000\times (1-\frac{15}{100})^{x}[/tex]
