John, a somewhat cynical car buyer, tells you that he thinks the price of the car he just purchased will vary inversely with its age.  He draws the following graph to describe what he means.

1. Move the age slider around to determine the constant ratio between the car's age and its predicted value.  What is this constant of proportionality?

In this case, we are looking at inverse variation.  The equation here is y = k/x, or k=x*y.  Thus, the independent variable, x, is the age of the car (in years).  The dependent variable, y, is John's predicted value of the car (measured in thousands of dollars). If we take a few sample points, we find the following:

 

x	y	k=y*x	Here again we see that k is a constant.
1	30	1*30 =30
2	15	2 * 15 = 30
5	6	5 * 6 = 30

 

2. How much will the car be worth in 10 years?  If he purchased the car when it was 1 year old, how much did he pay for it? Using John's formula, determine much will the car be worth in 30 years.

               y = 30/10 = 3, or $3,000 (using the scale)

               y=30/1 = 30, so he paid $30,000 for the car when it was 1 year old.

               y=30/30 =1, so it will be worth $1,000 in 30 years (which is actually amazing, unless it turns out to be a collector's item!)