A new machine costing $$54,000$ cash and estimated to have a $$9,000$ salvage value was purchased on January $1.$ The machine is expected to produce $3,000$ units of product during its $5-$year useful life. Calculate depreciation expense in the first year under the following independent situations.

$1.$ The company uses the units$-$of$-$production method and the machine produces $450$ units of product during its first year.

$2.$ The company uses the double$-$declining$-$balance method.

$3.$ The company uses the straight$-$line method.