$5.$ The radioactive isotope $(82$Sr$)$ has a half$-$life of $25\mathrm{.}4$ days. A sample containing this isotope has an initial activity at $($t

$0)$ of $4\mathrm{.}50108$ Ba$.$ Calculate the number of nuclei that will decay in the time interval between ty $=40\mathrm{.}0$ hours and t$2=$

$55\mathrm{.}0$ hours.