Radon, `._(86)^(222)Rn`, is a radioactive gas that can be trapped in the basement of homes, and its presence in high concnetrations is a known health hazard. Radon has a half-life of `3.83 days`. A gas sample contains `4.0 xx 10^(8)` radon atoms initially.
(a) How many atoms will remain after `12 days` have passed if no more radon leaks in? (b) What is the initial activity of the radon sample?