Question

After it is purchased, the value of a new car decreases $4,000 each year. After 3 years, the car is worth $18,000.

a. Write an equation that represents the value V (in dollars) of the car x years after it is purchased.
b. What was the original value of the car?

Answer 1

To answer the student's question about car value depreciation, an equation V = P - 4000x was established, which models the car's value decrease of $4,000 yearly. After 3 years, when the car's worth was $18,000, the original value was calculated to be $30,000.

Step-by-step explanation:

To solve the student's question regarding the depreciation of a car's value, we need to establish an equation that expresses the value V of the car x years after it is purchased, given that the car decreases in value by $4,000 each year.

Part A: Write the Equation

The general form for the equation that models this depreciation is:

V = P - 4000x

Where:
V is the value of the car x years after purchase,
P is the original value of the car,
And 4000x represents the total depreciation after x years.

Part B: Original Value of the Car

Using the information provided that after 3 years the car is worth $18,000, we plug in the values:

18000 = P - 4000(3)

This reduces to:

18000 = P - 12000

Adding 12000 to both sides:

P = 18000 + 12000

P = $30,000

The original value of the car was $30,000.