Final answer:
For Brown Company, straight-line depreciation is the most suitable method for depreciating long-term assets due to the consistent decrease in their annual revenue, which reflects a stable rate of asset usage or decline over time.
Step-by-step explanation:
The provided table showing the revenues of Brown Company over three years indicates a consistently decreasing amount of revenue each year. Considering this pattern, Brown Company should use straight-line depreciation for its long-term assets. This method spreads the cost of the asset evenly over its useful life, reflecting a steady decrease in revenues, which can be seen as an indication of predictable, steady use or decline in asset utility over time. On the contrary, double-declining-balance depreciation accelerates depreciation early on, which may not match Brown's revenue pattern, and units-of-production depreciation ties depreciation to usage, which isn't provided here. Lastly, first-in-first-out depreciation is a term not applicable to depreciation methods as it is related to inventory management, not asset depreciation.