Chen Corporation purchased equipment on January $1,$ year $1,$ for $$100,000.$ The equipment was depreciated using the units$-$of$-$output method. During years $1$ and $2,$ respectively, Chen recorded depreciation expense of $$10,000$ and $$30,000.$ During year $3,$ Chen changed to the straight$-$line depreciation metlYod and estimated that the equipment had a remaining useful life of $10$ years and no residual value. What is the depreciation expense Chen should report during year $3?$

$$6,000$

$$10,000$

$$0$

$$4,000$