Perdue Company purchased equipment on April $1$ for $$50,490.$ The equipment was expected to have a useful life of $3$ years, or $7,560$ operating hours, and a residual value of $$1,350.$ The equipment was used for $1,400$ hours during Year $1,2,600$ hours in Year $2,2,300$ hours in Year $3,$ and $1,260$ hours in Year $4.$ Determine the amount of depreciation expense for the years ended December $31,$ Year $1,$ Year $2,$ Year $3,$ and Year $4,$ by $($a$)$ the straight$-$line method, $($b$)$ the units$-$of$-$activity method, and $($c$)$ the double$-$declining$-$balance method.