Question

National Textile installed a new textile machine in one of its factories at a cost of $250,000. 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 Ith year of use (Osts 10). v(t) = -24,0001 + 250,000 x

Answer 1

The required expression is
`y=250,000-24,000 t`

Explanation:

Consider the provided information.

National Textile installed a new textile machine in one of its factories at a cost of $250,000.

That means for 0 year the cost of the machine is $250,000.

This can be written as: (0, 250,000)

Over 10 years with a scrap value of $10,000

That means for 10 year the cost of the machine is $10,000.

This can be written as: (10, 10,000)

Now first find the rate of change:

Rate of change=m=
`(Rise)/(Run)=(10,000-250,000)/(10-0)`

Rate of change=m=
`(Rise)/(Run)=(-240,000)/(10)`

Rate of change=m=
`(Rise)/(Run)=-24,000`

Now use the point-slope form of an equation of a line with the point (0, 250,000), we can find the required expression.

`(y-250,000)=-24,000(t-0)`

`y-250,000=-24,000 t`

`y=250,000-24,000 t`

Hence, the required expression is
`y=250,000-24,000 t`