The function f(x) = 12,500 – 800x represents the resale value of Joe’s car as it depreciates

Question

The function f(x) = 12,500 – 800x represents the resale value of Joe’s car as it depreciates x years after its purchase. The table below shows the value of Adam’s car as it depreciates linearly x years after its purchase

years after purchase 1. 3. 5

resale value. 11,200. 7,400. 3,600

Which statement accurately compares the amount the resale value goes down each year for the two cars?

 

What is the difference between the amount the resale value changes each year for the two cars?

A. Adam's car decreases $1,900 more than Joe's does each year

B. Adam's car decreases $1,100 more than Joe's does each year

C. Joe's car decreases $800 more than Adam's does each year

D. Joe's car decreases $1,100 more than Adam's does each year

Answer 1

Hello, Anna,

Joe's car depreciates according to: f(x) = 12,500 - 800x, where x is years since purchase. The purchase price was $12,500, when x = 0. the 800 is the depreciation per year.

We can determine a depreciation equation for Adam's car by looking at the value change over time. The depreciation between years 1 and 3 was ($11,200 - $7,400) = $3,800. Divide by the two years to get the yearly depreciation (= $1,900/year). If we add the 1900 to the value of Adam's carat the end of the first year, we find the initial price to be $13,100.

No we can set up an equation for Adam's car, just as we have for Joe's car.

f(x) = 13,100 - 1900x

He paid $13,100 and it depreciates at a rate of $1900/year.

We can check this equation by trying the years for which we have the data (years 1, 3 , and 5). The values match the ones given in the problem, so our equation is valid, as far as we can tell from what we know.

My table won't fit in this box, but you can set up a spreadsheet to do the calculations.

We see that Adam's car depreciates at $1900/year, which is $1100 more than Joe's depreciation of $800/year.

Bob