Question

In 2010, National Textile installed a new textile machine in one of its factories at a cost of $200,000. The machine is depreciated linearly over 10 years with a scrap value of $10,000.

(a) Find an expression for the textile machine's book value in the t th year of use
(0 ≤ t ≤ 10).

Answer 1

`V(t)=-19,000t+200,000`

Explanation:

Let V(t) be the value of machine after t years and t represents the number of years after 2010.

We are given the value in the beginning as 200,000. We are also given scrap value (value at the end of period) as 10,000.

So we need to find a linear function with points (0, 200000) and (10,10000)

Let us find slope of our line using our given points.

`m=(10,000-200,000)/(10-0)`

`m=(-190,000)/(10)`

`m=-19,000`

Since we know that the slope-intercept form of equation is in form:
`y=mx+b`, where,

m = Slope of line,

b = The y-intercept or initial value.

We can see that initial value of machine is $200,000, so substituting m=-19,000 and b = 200,000, we will get our equation as:

`V(t)=-19,000t+200,000`

Therefore, the equation
`V(t)=-19,000t+200,000` represents the the textile machine's book value in the th year of use.