Question

For tax and accounting purposes, corporations depreciate the value of equipment each year. One method used is called "linear depreciation," where the value decreases over time in a linear manner. Suppose that two years after purchase, an industrial milling machine is worth $670,000, and five years after purchase, the machine is worth $130,000. Find a formula for the machine value V (in thousands of dollars) at time t ≥ 0 after purchase.

Answer 1

Answer:

Explanation:

The method we have to use is linear depreciation.

We will first find the slope:

$Slope=\frac{V_{2}-V_{1}}{Y_{2}-Y_{1}}$

where:

V_2 is the machine value after 5 years.

V_1 is the machine value after 2 years.

Y_1 = 2 years

Y_2 = 5 years

$Slope=\frac{130000-670000}{5-2}$

$Slope=-180,000$

Now:

$Slope=\frac{V_{2}-V}{Y_{2}-Y}$

where:

V is the machine value at  t ≥ 0.

Y is the years at  t ≥ 0.

$-180,000=\frac{130000-V}{5-Y}$

Rearranging the above expression.

$V=130000+180000(5-Y)$

Formula for the machine value = $V=130000+180000(5-Y)$