Question

A piece of equipment used in a landfill has an original value of $200,000. After two years of use, the piece of equipment is valued at $150,000.

A) If the depreciation of the equipment is assumed to be linear, find an equation to relate the value (V) of the equipment over time (t).
B) What would the value of the piece of equipment be after 6 years?
C) In how many years would the value of the piece of equipment be $0 ?

Answer 1

The equation to relate the value of the equipment over time can be found using the formula for the equation of a line. The equation is V = -25,000t + 200,000. The value of the piece of equipment after 6 years would be $50,000 and the value of the piece of equipment would be $0 after 8 years.

Step-by-step explanation:

The equation to relate the value (V) of the equipment over time (t) can be found using the formula for the equation of a line. We can use the two given data points: (0, $200,000) and (2, $150,000).

First, we need to find the slope of the line. The slope is equal to the change in y-coordinates divided by the change in x-coordinates. Slope (m) = (150,000 - 200,000) / (2 - 0) = -50,000 / 2 = -25,000.

Next, we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept. We can substitute one of the given points to find the value of the y-intercept. Using the point (0, $200,000): 200,000 = -25,000(0) + b, b = 200,000.

Therefore, the equation to relate the value of the equipment over time is: V = -25,000t + 200,000.

B) To find the value of the piece of equipment after 6 years, substitute t = 6 into the equation: V = -25,000(6) + 200,000, V = -150,000 + 200,000 = $50,000.

C) To find the number of years when the value of the equipment is $0, set the equation equal to 0 and solve for t: 0 = -25,000t + 200,000. -25,000t = -200,000, t = 8.