Question

A new car worth 24,000 is depreciating in value by $3,000 per year. Complete parts a. & b. A. Write a formula that models the cars value, y, in dollars, after x years. Y= B. Use the formula from part (a) to determine after how many years the cars value will be $12,000. After ___ years, the cars value will be $12,000

Answer 1

24000-12000=12000. 12000/3000=4. 4 years

Answer 2

A) y = 24000 - 3000 x

B) 4 years

Explanation:

Part A

We need to write a formula for the car value y, after x years, knowing that:

• The initial car values is $24,000
• The car value depreciates (decreases) $3,000 per year

So to calculate the car value after x years we must subtract to the initial car value (fixed independent term) how much the value has depreciated, that is $3000 multiplied by the amount of years x.

So the car value will be calculated as:

y = 24000 - 3000 x

Part B

The question asks after how many years the car value will be $12000

So, y = 12000

we need to calculate the years x

Lets replace in the formula and solve for x:

12000 = 24000 - 3000 x

we must isolate x by doing the opposite operations:

12000 - 24000 = 24000 -24000 -3000 x

-12000 = -3000 x

-12000 / (-3000) = -3000 x / (-3000)

4 = x

After 4 years the car value will be $12000