Radon$-222(22286$ Rn$)$ is a radioactive gas with a half$-$life of $3\mathrm{.}82$ days. A gas sample contains $4\mathrm{.}9108$ radon atoms initially. a$)$ Determine how many radon atoms will remain after $12$ days. Question $8,$ chap $151,$ sect $5.$ part $2$ of $210$points b$)$ Determine how many radon nuclei will have decayed by this time.