The radioactive isotope sodium$-24$ is used as a tracer to measure the rate of flow in an artery or vein. The half$-$life of sodium$-24$ is $14\mathrm{.}9$ hours. Suppose that a hospital buys a $20-$g sample of sodium$-24.$

$($a$)$ How much of the sample will remain after $48$ hours? $($Round your answer to two decimal places.$)$

$($b$)$ How long will it be until only $1$ gram remains? $($Round your answer to the nearest whole number.$)$