Question

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?

Answer 1

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)