Given functions are
[tex]s(n)=2(1.1)^n+5_{}[/tex][tex]d(n)=4(1.08)^n+3[/tex]The total number of ducks and swans in the lake after n months can be determined by adding the functions s(n) and d(n).
[tex]t(n)=s(n)+d(n)[/tex][tex]t(n)=(2(1.1)^n^{}+5)+(4(1.08)^n+3)[/tex][tex]t(n)=2(1.1)^n+5+4(1.08)^n+3[/tex][tex]t(n)=2(1.1)^n+4(1.08)^n+5+3[/tex][tex]t(n)=2(1.1)^n+4(1.08)^n+8[/tex]Taking 2 as common, we get
[tex]t(n)=2\lbrack(1.1)^n+2(1.08)^n+4\rbrack[/tex]Hence The total number of ducks and swans in the lake after n months is
[tex]t(n)=2\lbrack(1.1)^n+2(1.08)^n+4\rbrack[/tex]