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

a$.$ Estimate the population of this group for the year $2010.$

b$.$ What is the instantaneous rate of change of the population when $t=10?$

a$.$ The population in $2010$ is $$ million people.

$($Round to three decimal places as needed.$)$