Question

Diamond recently bought a car. Her research shows the car will depreciate an average of $1,200 per year. She knows that after 8 years, her car will be worth $22,600. Let x represents the number of years Diamond owns the car and y represent the value of the car.

Write a function that represents the value of car after x years.

Answer 1

To represent the value of Diamond's car over time, we determine a linear depreciation function using the slope of $1,200 yearly depreciation and the given point (8 years, $22,600 in value). The function is y = -$1,200x + $32,200, indicating the car's initial value and its depreciation over time.

Step-by-step explanation:

Writing a Function to Represent Car Value Depreciation

To write a function that represents the value of Diamond's car after x years, we'll use the information provided: Diamond's car depreciates $1,200 every year, and after 8 years, the car will be worth $22,600. We can use these two points to determine the linear depreciation function.

First, let's identify the annual depreciation as the slope of the function: $1,200 per year. Next, we'll use the point (8, $22,600) to solve for the y-intercept, which represents the initial value of the car. The linear function will be of the form: y = mx + b, where m is the slope and b is the y-intercept.

Now, we plug in values for x and y from the point (8, $22,600):

$22,600 = (-$1,200) × 8 + b

We solve for b, which gives us:

b = $22,600 + ($1,200 × 8)b = $22,600 + $9,600b = $32,200

This means the initial value of the car is $32,200. The final depreciation function is:

y = -$1,200x + $32,200

This function tells us the value of Diamond's car (y) after x years of ownership.