# Suppose that a company has just purchased a new computer for $1500 the company chooses to depreciate using the straight-line

###### Question:

## Answers

we are given that

Suppose that a company has just purchased a new computer for $1500

so, we have (0,1500)

The company chooses to depreciate using the straight-line method for 5 years

so, (5,0)

(a)

Let's assume the book value of the computer as the function of its age is y

time in years is x

(0,1500)

x1=0 , y1 =1500

(5,0)

x2=5 , y2=0

Firstly, we will find slope

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

we can plug values

[tex]m=\frac{0-1500}{5-0}[/tex]

[tex]m=-300[/tex]

now, we can use point slope form of line

[tex]y-y_1=m(x-x_1)[/tex]

we can plug

[tex]y-1500=-300(x-0)[/tex]

[tex]y-1500=-300x[/tex]

[tex]y=-300x+1500[/tex].............Answer

(b)

we are given time limited to 5 years

so, domain is

[tex][0,5][/tex]

(c)

we can draw graph

(d)

we can plug x=3

[tex]y=-300*3+1500[/tex]

[tex]y=600[/tex]...........Answer

(e)

we can set y=1600

and then we can solve for x

[tex]1600=-300x+1500[/tex]

x is negative

so, it is undefined

[tex]Suppose that a company has just purchased a new computer for $1500 the company chooses to depreciate[/tex]

Solution-

The company purchased a new computer for $1500 and chooses to depreciate using the straight-line method for 5 years.

a-

As the value is depreciating, so its slope will be -ve.

[tex]Slope =- \frac{1500}{5}=-300[/tex] ( ∵ The value of 1500 will depreciate in 5 years )

y-intercept = 1500 ( ∵ At the beginning when x=0, y=1500)

Linear equation of the system,

y = mx +c ,

where,

m = slope = -300,

c = y-intercept = 1500

Putting the values,

[tex]y=-300x+1500[/tex]

[tex]\Rightarrow y=1500-300x[/tex]

b-

The implied domain of the function is 1≤x≤5 or [1,5]

c-

Follow the attachment attached herewith for the graph.

d-

Here,

y = the value of the computer

.

x = number of years depreciated = 3

Putting the values in the linear equation,

y = 1500-300(3) = 1500-900 = 600

∴ The book value of the computer after 3 years is $600.

e-

Here given that,

y = value of computer = 1600

x = asked = ??

Putting the values in the equation,

1600 = 1500 - 300x

⇒ 100= -300x

⇒ x= -3

∴ As the x is in negative, i.e it is impossible for the computer to be worth of 1600. It happens also because as the value is depreciating, it will always be less than 1500.