Asmall business purchases a
piece of equipment for $875. after 5 years the equipment will be outdated, having no value.

(a) write a linear equation giving the value of the equipment y in terms of the time
(b) find the value of the equipment when x=2
(c) estimate (to two-decimal-place accuracy) the time when the value of the equipment is $200.

It is assumed that the equipment will lose value at a constant yearly rate. Then we can find a linear function to represent the value of the equipment.

The rate at which the equipment loses value is $ 875 / 5 years =$ 175 / year.

a) y = 875 - 175x

b) x = 2 => y = $875 - [S175/ year] (2year) = $875 - $350  = $ 525

c) y = 200 = 875 - 175x => x = [875 - 200] / 175 = 3.86 years

The decimal expansion would be .27 repeated