How to Calculate the Decrease in Value of a Car Over Time

The value of a particular car decreases at a constant rate. If the car is worth $15,000 three years after its original purchase date and $10,000 five years after its original purchase date, what was the value of the car on its original purchase date?

Let’s denote the original purchase date as year 0

Let’s denote the original purchase date as year 0. We can set up a linear equation to represent the decrease in value of the car over time.

Let x be the number of years after the original purchase date (x = 0 represents the original purchase date).
Let y be the value of the car at x years after the original purchase date.

We are given two points on the line:
(3, $15,000) and (5, $10,000).

Using the formula for the equation of a line, we can find the equation to represent the decrease in value:

(y – y1) = [(y2 – y1) / (x2 – x1)] * (x – x1)

Plugging in the values from the given points:
(y – $15,000) = [($10,000 – $15,000) / (5 – 3)] * (x – 3)

Simplifying the equation:
(y – $15,000) = [-$5,000 / 2] * (x – 3)
(y – $15,000) = -$2,500 * (x – 3)
y – $15,000 = -$2,500x + $7,500
y = -$2,500x + $7,500 + $15,000
y = -$2,500x + $22,500

This equation represents the decrease in value of the car over time.

To find the value of the car on its original purchase date (x = 0), we substitute x = 0 into the equation:
y = -$2,500(0) + $22,500
y = $22,500

Therefore, the value of the car on its original purchase date was $22,500.

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