The projected population of a certain ethnic group $($in millions$)$ can be approximated by $p(t)=38\mathrm{.}4(1\mathrm{.}024{)}^t$ where $t=0$ corresponds to $2000$ and $0t50.$

$($a$)$ Estimate the population of this group for the year $2030.$

$($b$)$ What is the instantaneous rate of change of the population when $t=30?$

$($c$)$ Interpret your answer to part $($b$).$