A piece of manufacturing equipment was purchased at the beginning of year $1$ for an original cost of $50,000.$ Over it's useful life, the equipment is expected to produce $40,000$ widgets as follows:

Year $1$: $4,000$ units

Year $2$: $10,000$ units

Year $3$: $12,000$ units

Year $4$: $8,000$ units

Year $5$: $6,000$ units

The asset will have a residual $($scrap$)$ value of $10\%$ of its original cost at the end of year $5.$ The usage of the asset varies over time and is dependent on the output. What is the year $5$ depreciation expense using the units of production approach?