On May $30,2021,$ Jane purchased a factory building to use for her business. In August $2022,$ Jane paid $$300,000$ for improvements to the building. Determine Jane's total deduction with respect to the building improvements for $2022.$

a$.$ $$4,815$

b$.$ $$4,173$

c$.$ $$2,889$

d$.$ $$25,000$