Question

Terrence buys a new car for $20,000. The value of the car depreciates by 15% each year. If f(x) represents the value of the car after x years, which function represents the car’s value?

Answer 1

20000*(0.85)^x

Explanation:

Answer 2

The function f(x) representing the value of car after x years is given by

`f(x)=\$ 20,000* (1-(15)/(100))^(x)`

Explanation:

Since value of car depreciates by 15% each year

Value of car after 1 year

`f(1)=value of new car *(1-(15)/(100))`

=>
`f(1)=\$ 20,000*(1-(15)/(100))`

Value of car after 2 year

`f(2)=\$ 20,000*(1-(15)/(100))*(1-(15)/(100))`

=>
`f(2)=\$ 20,000*(1-(15)/(100))^(2)`

Value of car after 3 year

`f(3)=\$ 20,000*(1-(15)/(100))*(1-(15)/(100))*(1-(15)/(100))`

=>
`f(3)=\$ 20,000*(1-(15)/(100))^(3)`

Similarly value of car after x years is

`f(x)=\$ 20,000* (1-(15)/(100))^(x)`