A desk was bought at a price of $830, and was sold 6 years later at a price of $140. Assuming the function is linear, find the depreciation formula and the value of the desk after 3 years.

Question

A desk was bought at a price of $830, and was sold 6 years later at a price of $140.   Assuming the function is linear, find the depreciation formula and the value of the desk after 3 years.

whpalmer4 · Answer

The value of the desk V(t) starts out at V(0) = 830.  After 6 years, the value V(6) = 140.  You have two data points specifying a line:  (0,830) and (6,140).  Use the formulas you just saw to find the equation of the line, then find V(3) (aka point (3,???)).

anonymous · Answer

im still confused

anonymous · Answer

^ If V(6)=140 V(3); which is half of V(6) should be 140/2

anonymous · Answer

ok so what would that answer be where does v come from?

whpalmer4 · Answer

V is just a function that gives you the value of the desk at time t...what you sell it for, in other words

whpalmer4 · Answer

but I don't think v(3) is going to be half of v(6)!  remember, the value goes down as time goes on.

I'm unsure as to whether the text/instructor is expecting a function showing the value after depreciation (what I've done above) or a function which shows the amount of depreciation, which you subtract from the starting value to get the remaining value.  In the latter case, your depreciation function would have a value of 0 at t = 0, and a value of 830-140 = 690 at t = 6.  At t = 3, one would expect it to be halfway between the value of 0 at t = 0 and the value of 690 at t = 6 because this is a linear relationship.

whpalmer4 · Answer

probably the latter approach is better, I guess, as it does ask for a depreciation function.  So, if D(t) is your depreciation function, D(t) = the equation of a line through (0,0) and (6,690), and the value of the desk at 3 years is $830 - D(3)

whpalmer4 · Answer

Maybe a picture will help:

whpalmer4 · Answer

No, because you're taking the whole value instead of the depreciation.  The desk has lost 830-140 = 690 in depreciation over the course of 6 years.  We are doing a linear depreciation here (in real life, there are a bunch of different ways of doing depreciation, depending on the financial goal), so after 1 year, we've depreciated 1/6 of 690 (= 115).  After 2 years, we've depreciated 2/6 of 690 (= 230), etc.

whpalmer4 · Answer

If you're thinking "doesn't that mean the depreciation formula is just 115 * the number of years?" give yourself a pat on the back.

whpalmer4 · Answer

Time for me to call it a night...good luck!

anonymous · Answer

I managed to squeeze information out of him bhow21, good luck!