Question

A small business buys a computer for $3700. After 4 years the value of the computer is expected to be $200. For accounting purposes the business uses linear depreciation to assess the value of the computer at a given time. This means that if V is the value of the computer at time t, then a linear equation is used to relate V and t.
(a) Find a linear equation that relates V and t.
(b) Sketch a graph of this linear equation.
(c) What do the slope and V-intercept of the graph
represent?
(d) Find the depreciated value of the computer 3 years from the date of purchase.

Answer 1

So what part is giving you trouble?

Answer 2

All of it

Answer 3

OK. Well, you need an equation, graph, and some data. So, with a word problem the first part is to get the numbers. What numbers and variables do you see in this?

Answer 4

$3700, 4 years, and $200

Answer 5

You missed one. The start time. 0 years. But they don't list it directly.

OK, you have two $ values and two years values. So, that sounds like (x,y) pairs to me! Then it is use two points to determine a line.

Answer 6

So which do you think should go on the x axis and which on the y?

Answer 7

(0,3700) (4,200)

Answer 8

=) Great! So, know how to use that to find an equation of a line?

Answer 9

y=mx+b

Answer 10

Yes, so first you need the slope, m.

Answer 11

m=-875

Answer 12

Doing great. Now, know how to use the slope and one point to find the equation of a line?

Answer 13

y=-875x+3700

Answer 14

And that is the answer to A. Just need to replace y with V and x with t.

Answer 15

ok great

Answer 16

So, know how to sketch that? You can do the equation or just use the points and draw a line.

Answer 17

so use the points i listed above?

Answer 18

Yes. Remember that V (The $ value) is the Y axis and t (time) is the x. Don't label them as x and y, but rather Time and Value. Then use those points. Obviously the scale will be a bit skewed or you would have to make a huge graph.

Answer 19

how do i do d

Answer 20

Well, years is a time value. So, V(t) becomes V(3). That make sense?

Answer 21

kinda

Answer 22

Well, you worked up the formula \(V(t)=-875t+3700\). If you plug in 3, what do you get?

Answer 23

the equation of the line is wrong

Answer 24

You originally wrote it as \(y=-875x+3700\) and \(V(t)=-875t+3700\) is te same thing. From the data you gave, that is the correct equation.

Answer 25

It keeps saying its wrong

Answer 26

Did you use x and y or V and t?

Answer 27

v and t

Answer 28

it may be the website thats wrong

Answer 29

Hmmm.... not sure then.

\((0,3700)\) and \((4,200)\)

\(\dfrac{\Delta y}{\Delta x} = \dfrac{3700-200}{0-4} \implies \)

\(\dfrac{\Delta y}{\Delta x} = \dfrac{3500}{-4} \implies \)

\(\dfrac{\Delta y}{\Delta x} = -875 \)

So that is m. No question.

Answer 30

Make sure to try a capitol V. They have it that way in the question.

Answer 31

\(V-V_1=m(t-t_1) \implies \)

\(V-3700=-875(t-0) \implies \)

\(V-3700=-875t \implies \)

\(V=-875t+3700 \)

Answer 32

So, yah, it is something odd with that submission site.