Question

A car was purchased for $27,000Each year since, the resale value has decreased by 22% Let be the number of years since the purchase. Let y be the resale value of the car, in dollars Write an exponential function showing the relationship between y and

Answer 1

Hello!

Let's write some important information:

• Initial value: $27,000

,

• decrease each year (22%)

,

• y: resale value

,

• t: time in years

Knowing it, let's think:

If every year the value decreases by 22%, we can say that the car value is 78% of the last value, right?

So, we can write it as:

$y=(\mathrm{Initial}\text{ }\mathrm{Cost)}\cdot(\mathrm{Rate}\text{ }\mathrm{of}\text{ }\mathrm{Decrease}^{\mathrm{number}\text{ }\mathrm{of}\text{ }\mathrm{years}})$

Let's replace it with the values:

$\boxed{y=27,000\cdot(0.78^t)}$