© Nuffield Foundation 2011 Nuffield Free-Standing Mathematics Activity What’s it worth? © Rudolf Stricker

© Nuffield Foundation 2010 Most cars lose value from the day they are bought. What’s it worth?

© Nuffield Foundation 2010 What’s it worth? What does ‘depreciation’ mean? At what age does a car lose its value most quickly? What shape would you expect a graph of value against age to be?

© Nuffield Foundation 2010 What’s it worth? Depreciation in value of a Toyota Aygo hatchback Age ( t years) Value of car (£ V )

© Nuffield Foundation 2010 What’s it worth? The rate of depreciation is equal to the gradient of the curve. Is the gradient positive or negative? When is the rate of depreciation greatest? When is it least?

© Nuffield Foundation 2010 What’s it worth? Model A The value of the car depreciates at a constant rate. Model B The rate of depreciation is proportional to the age of the car. Model C The rate of depreciation is proportional to the value of the car. Model D The rate of depreciation is inversely proportional to the age of the car. Think about…. Which of these do you think are likely to be good models?

© Nuffield Foundation 2010 Model E The rate of depreciation is inversely proportional to the square root of the age of the car. Model F The rate of depreciation is inversely proportional to the value of the car. Model G The rate of depreciation is proportional to the square of the value of the car. Model H The rate of depreciation is proportional to the square root of the value of the car. Think about…. Which of these do you think are likely to be good models?

Reflect on your work Which model(s) do you prefer? Explain your preference. Do this by comparing the features of these model(s) with those of models you have rejected. What’s it worth?