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?

1 Answer
Mar 29, 2015

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)