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

$=12000-\frac{12000\times10}{100}$

$=0.9\times12000$

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 }\times10}{100}$$=0.9\times12000-\frac{0.9\times12000\times10}{100}$

$=0.9\times12000\times\frac{100}{100}-\frac{0.9\times12000\times10}{100}$

$=\frac{0.9\times12000\times100-0.9\times12000\times10}{100}$

$=\frac{0.9\times12000(100-10)}{100}$

$=\frac{0.9\times12000\times90}{100}$

$=0.9\times0.9\times12000$

$=0.9^2\times12000$

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

$f(x)=12000\times0.9^x$

Hence the required equation is

$f(x)=12000\times0.9^x$