What you are looking for is a function that presents the age (in months or odometer reading) of the car along the X-axis, and the price of the car along the Y-axis. This function is not going to be the simple linear relationship that you might desire and would be easiest to express and understand. The function will be one that starts high, drops swiftly for the first couple of months (depreciation, why buy a car with 500 miles on it for nearly the same price as a new car?). Then the price drops more gradually, until the car is about 3 years old/50K miles, where it has reached about 50-60% of the original price. That price point varies by make and model of car (some cars hold more value, others less, depending upon their desirability and utility).
Were you able to (accurately) graph this function over the useful life of the car, you would find that it would have discontinuities (jumps of $1000's of dollars) as events happened to the car (accidents, breakdowns), as well as smoother periods. As a car approaches major event points (replace the tires, replace the timing belt, replace the alternator, brakes, rotors, catalytic converter, hybrid battery), the price will drop more, and (may) jump back above the price trend line (function graph) after each repair or replacement occurs.
Each make and model of car has a similar graph, although the price changes at different rates -- so that were you able to scale all vehicles to the same price, and superimpose each age/price graph, you would observe that they would differ by make, model, type, options, even color. But you may note (as I have) that every vehicle follows a similar shaped curve.
There is also a value function (subjective to you) that you would place on the car. Since you seek to use the car, the value you place on the car is a simpler function, where you judge the value to be the cost to acquire the car, costs to make expected repairs on the car, less residual sale price. And this value function would depend upon the expected remaining life of the car. You may sketch this function as a straight line from the original purchase price to the expected residual sale price (when you finally dispose of the vehicle).
And every other person seeking to buy a similar car in the used car market also has a value function for the car, some starting at decided points (want to buy a car less than price P) different than yours, and some ending at decided points (keep for specified duration), at differing ages or values. Their functions differ from yours, and are part of the reason why the price fluctuates so much. Some people want to buy newer used cars (fewer expected problems), others want to buy older used cars (lower purchase price).
The challenge and the problem you are trying to solve, is one of two approaches to saving money. One is that you want to find the inflection point, where the slope of the price curve levels out (becomes less negative). At that point in the price curve, you would pay less money for the usage of the car. Or you may superimpose your value function and the price function for a car onto the same graph, and as a rational person you would seek to buy the car at the age when the difference (gap) between the price of the car, and (your) value of the car is large (thus saving the most money). But everyone in the used car market is also trying to do the same, but with different factors which they value, and that is where the variations in the price function of the car occur.
Factors people who choose to buy used cars, and the priority they place on those factors vary,
- Some people seek to save the most money
- Some choose to minimize the cost to own the car
- Some want to own newer cars
- Some need to buy cheaper cars
- Some try to avoid paying repair bills
- Some desire certain makes, models, styles, options, or colors
My approach on the past several car purchases has been to find a car with low odometer and a price around 50% of the original price.