An isotope of sodium, $24$Na $,$ has a half$-$life of $15$ hours. A sample of this isotope has mass $2$ g$.$

$($a$)$ Find the amount remaining after $60$ hours.

$($b$)$ Find the amount remaining after t hours.

$($c$)$ Estimate the amount remaining after $4$ days.

$($d$)$ Use a graph to estimate the time required for the mass to be reduced to $1$ mg$.$