The function $R(t)=t^a{e}^{-t},$ with $a>0,$ is defined in the domain

$($a$)$ For each value of $a,$ find the global $($absolute$)$ maximum and minimum of $R(t)$ exactly. Verify your result with a printout of a labeled plot generated by a plotting utility. $($i$)a=2$ii$a=5$

$($b$)$ Briefly describe the effect of the value of $a$ on the graph of $R(t).$ In particular, how do the locations and values of the minimum and maximum depend on a for $a>0?$