Question $14(2$pt$)$

Consider the following formal language. Provide an automaton that recognizes it$.$

$=\{a,b\}$

$L=\{abb,$aabb,aaabb,aaaabb,dots$\}$

Question $15(2pt)$

Can you make an automaton that recognize the same sentences as the one in question $11,$ but is smaller $($i$.$e$.,$ uses fewer nodes or arcs$)?$ If you think so$,$ provide a simpler automaton. If you think not, explain why not.