A small bulb is rated at $8\mathrm{.}8$ W when operated at $123$ V$.$ The tungsten filament has a temperature coefficient of resistivity a $=4\mathrm{.}5$ x $10-3/$C$.$ When the filament is hot and glowing, its temperature is $128$C$.$ Calculate the following $($In canvas enter only the answer to part a$)$

a$)$ The resistance of the filament when it is at the operating temperature.$$

b$)$ The resistance when the temperature of the filament drops to $20$C $($i$.$e$.$ when the lamp is off$).$

c$)$ At $10$ cents per kWh$,$ what will be the cost of operating the light$-$bulb for $100$ hours.