Question

You recently bought a new car and are curious how much it’s value drops over time. You do some research and find out that your brand of car depreciates 10% per year and you bought it new for $12,000. Write an exponential equation to represent the value of the car, f(x), based on the number of years since you bought it

Answer 1

Given that price of the car is $12000 and depreciates is 10%.

After one year the value of the car is

`=12000-(12000*10)/(100)`

`=0.9*12000`

After two years the value of the car is

`=\text{the value of car at first year-}\frac{the\text{ value of the car at first year }*10}{100}`
`=0.9*12000-(0.9*12000*10)/(100)`

`=0.9*12000*(100)/(100)-(0.9*12000*10)/(100)`

`=(0.9*12000*100-0.9*12000*10)/(100)`

`=(0.9*12000(100-10))/(100)`

`=(0.9*12000*90)/(100)`

`=0.9*0.9*12000`

`=0.9^2*12000`

proceeding this way, we get the car value f(x) for x number of years is

`f(x)=12000*0.9^x`

Hence the required equation is

`f(x)=12000*0.9^x`