Refer to section $5\mathrm{.}3$ for the relevant formulas and modeling techniques for half$-$life and compound interest. Show your work solving symbolically.

$2$ Tritium has a half$-$life of $12$ years.

a$.$ If an initial sample of $15$ grams is present, find a function $T(x)$ that represents the amount remaining, in grams, after $x$ years.

$T(x)=$

b$.$ Use your function to determine the amount of time it takes for the Tritium to decay to $5$ grams.