How do you determine the value of an x-ray machine after 5 year if it cost $216 thousand and Margaret Madison, DDS, estimates that her dental equipment loses one sixth of its value each year?

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Answer 1 · 2015-03-29T13:32:28

Each year the value of a piece of equipment becomes $5/6$ of its previous year value.

Initial value = 216 thousand dollars
Value after 1 year $= (26)*5/6$ thousand dollars

Value after 2 years $= ((26)*5/6)*5/6$ thousand dollars

Value after 3 years $=(((26)*5/6)*5/6)*5/6$ thousand dollars

Value after 4 years $=((((26)*5/6)*5/6)*5/6)*5/6$ thousand dollars

Value after 5 years $=(((((26)*5/6)*5/6)*5/6)*5/6)*5/6$ thousand dollars

Or more simply (and hopefully obviously by now)
Value after 5 years $= 26 *(5/6)^5$ thousand dollars

($10,449 to the nearest dollar, if this is important)