Question

After how many years will the car's value be $18,020 if the price of a certain automobile in 2003 was approximately $30,200 with a depreciation of $2,030 per year?

Answer 1

6 years

Explanation:

Let X be the car's value, and X(t) is the car's value as a function of time, in years.

We are told that depreciation of $2,030 occurs every year. So we can write:

X(t) = $30,200 - (t)*($2,030), where t = 0 when the car had a value of $30,200.

To find how many years until the car's value reaches $18,020, set X(t) to $18,020 and solve the equation for t:

X(t) = $30,200 - (t)*($2,030)

$18,020 = $30,200 - (t)*($2,030)

$30,200 - (t)*($2,030) = $18,020

- (t)*($2,030) = $18,020 - $30,200

- (t)*($2,030) = - $12,180

-t = - $12,180/($2,030)

t = 6 years