Finding the Value of an Industrial Milling Machine Using Linear Depreciation

[!Jon Snow!]

Homework Statement

For tax and accounting purposes, corporations depreciate the value of equipment each year. One method used is called "linear depreciation," where the value decreases over time in a linear manner. Suppose that two years after purchase, an industrial milling machine is worth $830,000, and five years after purchase, the machine is worth $500,000. Find a formula for the machine value V (in thousands of dollars) at time t ≥ 0 after purchase.

Homework Equations

v=?

The Attempt at a Solution

This is what I got;

At T=2 V=830,000
At T=5 V=500,000

V-500,000 =[T-5][500,000-800,000]/[5-2]
C-500,000=[T-5][330,000]

Is that right?

 

[HallsofIvy]

Was that "C" in the last equation a typo?

You have the right formula (point- slope which I assume was given in your book) but your arithmetic is terrible! (500,000- 800,000)/(5- 2) is NOT 330,000!

 

[!Jon Snow!]

Was that "C" in the last equation a typo?

You have the right formula (point- slope which I assume was given in your book) but your arithmetic is terrible! (500,000- 800,000)/(5- 2) is NOT 330,000!

Yes, it was a typo i meant to say "v".

Sorry, I typed this late last night.

V-500,000 =[T-5][500,000-830,000]/[5-2]
V-500,000=[T-5][-330,000]

 

[HallsofIvy]

Yes, so it is 830,000, not 800,000 and the fraction is negative. That is correct.
(The fact that this is depreciation tells you that the slope is negative.)