Question

A new building that costs $1,000,000 has a useful life of 25 years and a scrap value of $600,000. Using straight-line depreciation, find the equation for the value V in terms of t, where t is in years. (Make sure you use t and not x in your answer.)
V(t) =



Find the value after 1 year, after 2 years, and after 20 years.

Value after 1 year $
Value after 2 years $
Value after 20 years $

Answer 1

You have two points, the starting point (0, 1, 000,000) and the end point (25, 600,000)

Find the slope, which id the difference in Y over the difference in x:

m = (600,000 - 1,000,000) / (25-0)

= -400,000 / 25

= -16,000

Now you have V -1,000,000 = -16,000(x-0)

Rewrite in terms of V(t):

V(t) = -16,000t + 1,000,000

Now replace t with the years and solve:

1 year = V(1) = -16000(1) + 1,000,000 = -16,000 + 1,000,000 = $984,000

2 years = V(2) = -16,000(2) + 1,000,000 = -32,000 + 1,000,000 = $968,000

20 years = V(20) = -16,000(20) + 1,000,000 = -320,000 + 1,000,000 = $680,000