Question

a small business buys a computer for $4700. after 4 years the value of the computer is expected to be $200. for accounting purposes the business uses linear depreciation to assess the value of the computer at a given time. this means that if v is the value of the computer at time t, then a linear equation is used to relate v and t. find a linear equation that relates v (in dollars) and t (in yr).

Answer 1

The linear equation that relates the value of the computer and the time is v = -1125t + 4700.

Step-by-step explanation:

To find a linear equation that relates the value of the computer, v, and the time, t, we need to use the given information.

According to the question, the computer is bought for $4700 and after 4 years, its value is expected to be $200.

We can use the slope-intercept form of a linear equation, y = mx + b, where y represents the value of the computer (v), x represents the time (t), m is the slope, and b is the y-intercept.

Using the given information, we can set up the equation as follows:

v = mt + b

Since the initial value of the computer is $4700 at time t=0, the y-intercept is $4700, so b = 4700.

Next, we need to find the slope (m) by finding the change in value (Δv) over the change in time (Δt).

Δv = 200 - 4700 = -4500 (decrease in value)

Δt = 4 - 0 = 4 years

Now, we can calculate the slope:

m = Δv / Δt = -4500 / 4 = -1125

Substituting the values of m and b into the equation, we get:

v = -1125t + 4700

Therefore, the linear equation that relates the value of the computer (v) and the time (t) is v = -1125t + 4700.