In the straight-line method of depreciation used in plant economics, the value of a property decreases with time in which manner?

Introduction / Context:Depreciation methods allocate an asset’s cost over its service life for accounting and economic evaluation. The straight-line method is one of the most common due to its simplicity and uniform annual charges. Recognizing how asset value changes under this method is key for book-keeping and profitability analysis.

Given Data / Assumptions:

• Asset has original cost P and salvage value S.
• Service life is n years.
• Annual charge is constant throughout the life.

Concept / Approach:In the straight-line method, annual depreciation D is constant: D = (P - S) / n. The book value after t years is BV(t) = P - D * t, a linear function of time. Thus, the decrease in value is linear, not exponential or logarithmic.

Step-by-Step Solution:Compute annual depreciation: D = (P - S) / n (constant each year).Book value update: BV(t) = P - D * t.Linear dependence on t indicates a straight-line decline in value from P to S over n years.

Verification / Alternative check:Plotting BV(t) versus t yields a straight line from (0, P) to (n, S), confirming linear behavior. This contrasts with declining-balance methods that show faster early depreciation (nonlinear curves).

Why Other Options Are Wrong:Non-linearily, exponentially, logarithmically: These describe other depreciation or decay behaviors, not the constant-amount-per-year decrease of straight-line.

Common Pitfalls:

• Confusing book value trends of straight-line with declining-balance methods.
• Ignoring salvage value when computing annual charges.
• Mixing economic depreciation (market value changes) with accounting depreciation schedules.

Final Answer:linearly