Question

A computer system was purchased by a small business for $12,000 and, for tax purposes, is assumed to have a salvage value of $2,000 after 8 years. If its value is depreciated linearly from $12,000 to $2,000, find the linear equation that relates the value V in dollars to the time t in years.

Answer 1

`v(t)=-1250t+12000`

Explanations:

The linear equation that relates the value V in dollars to the time t in years can be expressed as;

`v(t)=mt+b`

where m is the slope

b is the "y-intercept"

If the value went from $12,000 at time t = 0, this can be written in a coordinate form as (0, 12000)

If the value depreciates linearly to $2000 after 8 years, this is expressed in coordinate form as (8, 2000)

Next is to get the slope of the line passing through the coordinate point (0, 12000) and (8, 2000)

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ m=(2000-12000)/(8-0) \\ m=-(10000)/(8) \\ m=-1,250 \end{gathered}`

Next is to get the y-intercept of the line.

Substitute the coordinate (0. 12000) and m = -1,250

`\begin{gathered} 12,000=-1250(0)+b \\ 12,000=b \\ \text{Swap} \\ b=12,000 \end{gathered}`

Substitute m = -1,250 and b = 12,000 into the formula to have:

`v(t)=-1250t+12000`

This gives the linear equation that relates the value V in dollars to the time t in years.