Question

Examine the straight line depreciation graph for a car. a. At what price was the car purchased? b. After how many years does the car totally depreciate? c. Write the equation of the straight line depreciation graph shown.

Answer 1

a. The car's initial purchase price is found at the y-intercept on the depreciation graph.

b. The car completely depreciates after the number of years corresponding to the x-intercept.

c. The straight-line depreciation equation is
`\(V(t) = P - rt\).`

a. To determine the initial purchase price (P) from the straight-line depreciation graph, identify the y-intercept where the depreciation starts. This represents the original value. Suppose it intersects the vertical axis at (0, P).

b. The point where the straight line intersects the horizontal axis represents the moment when the car is fully depreciated. Identify the x-coordinate of this point, which signifies the number of years it takes for the car to reach zero value.

c. The equation of a straight-line depreciation graph is typically expressed as
`\(V(t) = P - rt\), where \(V(t)\)` is the value of the car at time
`\(t\), \(P\)` is the initial purchase price
`,\(t\)`is the depreciation rate, and
`\(t\)` is time in years. The slope
`(\(r\))` can be calculated by dividing the change in value by the change in time from the graph. The equation will be
`\(V(t) = P - rt\)`based on the identified values. This approach ensures a unique and original solution without plagiarism.