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Dating Made Easier

Age 14 to 16 Challenge Level:

If a sum invested gains $10\%$ each year how long will it be before it has doubled its value?

If an object depreciates in value by $10\%$ each year how long will it take until only half of the original value remains?

Why aren't these two answers the same?

graph showing an appreciation and a depreciation curve

Is there a rate, used for both gain and depreciation, for which those two answers would actually be the same? How do you know?


If this problem caught your interest and you know some Stage 5 mathematics, this Plus article on Carbon Dating could be a good next step for you.