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

2 answers
Question:

Suppose that a company has just purchased a new computer for $1500 the company chooses to depreciate using the straight-line method for 5 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

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.

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