Question

PLEASE HELP!!!! Suppose that a company has just purchased a new computer for $3200 The company chooses to depreciate using the straight-line method for 4 years.

a) write a linear function that expresses the book value of the computer as the function of its age. (slop-intercept form)

b) what is the implied domain in of the function found in part (a) (interval notation)

c) graph the linear equation

d)what is the book value of the computer after 3 years. (near to the nearest dollar)

e) when will the computer be worth $1600

Answer 1

use
y=mx+b

Answer 2

but how will i get the problem in the y=mx+b

Answer 3

you have two given:
3200 and 4
translate those two into coordinates

Answer 4

if the value depreciates, it must mean that the slope will be negative

Answer 5

but how would u get it? im still confused what to do it with the the $3200 and the 4

Answer 6

year t | value V
0 3200
1 ____
2 ____
3 ____
4 0

The problem translates that the value of the computer at initial purchase at $3200 and after four-years at $0. We then need to find the depreciation value that made the computer's value to be $0 on the 4th year.

By means of intuition we can easily say that the depreciation value per year is $800. the value after a year is 3200 - 800 = 2400; 2nd year 2400 - 800 = 1600, and so on. But some problems are more complicated than this, so it is necessary for us to know how to translate them into equation.

Now, our first task is to think of how we would translate this into y=mx+b
y is your Value and x is your time/year. Look at the set up I provided in the beginning.

year t | value V
0 3200
1 ____
2 ____
3 ____
4 0

translate this into coordinates.
(0, 3200) (4, 0)

Our second task is to find the slope:
\[m=\frac{ \Delta y }{ \Delta x }=\frac{y_2-y_1 }{ x_2-x_1 }=\frac{ 0-3200 }{ 4-0 }=\frac{-3200 }{ 4 }=-800\]

Now that we have our slope we can rewrite our equation into more meaningful form.
\[V = -800t + 3200\]

Answer 7

I skipped the point-slope form and just re-write it into slope-intercept form

The point-slope form is
V-3200 = 800(t-0)

Answer 8

By finding our slope, it helps us to determine the depreciation in dollars per year. And the rest is just plugging in the values of the succeeding years.

Answer 9

what would the domain be then? i was thinking (0, 3200) ?

Answer 10

go back to the definitions on domain and ranges

Answer 11

domain would be the set of input and range would be the output. the equation. how would the domain be when the graph is decreasing. so would it be all real number if I was to look at the graph but if I look at the problem would it be starting at (3200 to something?? so if this confused you!! or would the domain be \[(-\infty, \infty)\]

Answer 12

http://finedrafts.com/files/math/precal/Larson%20PreCal%208th/Larson%20Precal%20CH1.pdf

start with page 39

Answer 13

Everything in there that I wrote gives you all the answer you need.
As you indicated DOMAIN is the the set of input (x) and the range is the set of output (y) with respect to the x. This means that one domain cannot have two ranges, because it will not be considered a function.

x y
year t | value V
0 3200
1 ____
2 ____
3 ____
4 0

DOMAIN= {0,1,2,3,4}

With our original given coordinates
(0, 3200) (4, 0)

DOMAIN = {0, 4}

Answer 14

oh! im sorry i keep thinking that 3200 was the input!!! now I get it!!!

Answer 15

would the domain be a close interval? [0,4]

Answer 16

if you were to graph instead of providing an interval notation, what would you put?

Answer 17

just graph the point (0,3200) to the point (4,0)

Answer 18

if you need to include the value 0 and 4 on the domain then it is close
[0, 4]

Answer 19

that's what I thought! THANK YOU!!

Answer 20

we are only graphing the domain