The book value of a machine is expressed by the equation V= 50,000 - 5000t

Question

The book value of a machine is expressed by the equation
V= 50,000 - 5000t
Where “V” equals the book value in dollars and “t” equals the age of the machine expressed in years.
(a) Identify the t and V intercepts.
(b) Interpret the meaning of the intercepts.
(c) Interpret the meaning of the slope.

Answer 1

Hi Madiha,

 

To find the intercepts you set one of the variables to 0 and solve for the other.

 

Lets find the t intercept,  we set V=0 and solve for t

 

V=50000-5000t

 

0 = 50000 - 5000t

 

5000t = 50000

 

t = 10 (divide both sides by 5000

 

OK so the t intercept (t,V) is (10,0)  

 

now for the V intercept

 

let t = 0 and solve for V

 

V= 50000 - 5000(0)

 

V = 50000

 

so the V intercept is (0,50000)

 

Meaning of intercepts

 

the t intercept shows the time when the book value becomes 0.  So in ten years the book value will be zero

 

the V intercept shows the original value of the machine.  It is when t = 0 or the starting point.

 

 

Meaning of the slope

 

For this equation the slope show us how much the book value is reduced for each year in time.  The book value is 5000 lower each year.

 

Hope this helps,

Tom