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

Answer 1

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

$m=\frac{y_2-y_1}{x_2-x_1}$

we can plug values

$m=\frac{0-1500}{5-0}$

$m=-300$

now, we can use point slope form of line

$y-y_1=m(x-x_1)$

we can plug

$y-1500=-300(x-0)$

$y-1500=-300x$

$y=-300x+1500$.............Answer

(b)

we are given time limited to 5 years

so, domain is

$[0,5]$

(c)

we can draw graph

(d)

we can plug x=3

$y=-300*3+1500$

$y=600$...........Answer

(e)

we can set y=1600

and then we can solve for x

$1600=-300x+1500$

x is negative

so, it is undefined