Question

stion 1 OT 5A researcher recorded the number of swans and the number of ducks in a lake every month. Function s represents the number ofswans and function d represents the number of ducks in a lake after n months.s(n) = 2(1.1)" + 5d(n) = 4(1.08)" + 3Which function can be used to determine the total number of ducks and swans in the lake after n months?o++t(n) = 2 (1.1)” + + 2(1.0R)" + 4Ot(n) = 2[2(1.1)" + (1.08)" + 4t(n) = 4 (1.1)” + 2(1.08)” + 2)ot(n) = 2 (1.1)”. + 2(1.08)" + 2]++SubmitReset

Answer 1

Given functions are

$s(n)=2(1.1)^n+5_{}$$d(n)=4(1.08)^n+3$

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).

$t(n)=s(n)+d(n)$

$t(n)=(2(1.1)^n^{}+5)+(4(1.08)^n+3)$

$t(n)=2(1.1)^n+5+4(1.08)^n+3$

$t(n)=2(1.1)^n+4(1.08)^n+5+3$

$t(n)=2(1.1)^n+4(1.08)^n+8$

Taking 2 as common, we get

$t(n)=2\lbrack(1.1)^n+2(1.08)^n+4\rbrack$

Hence The total number of ducks and swans in the lake after n months is

$t(n)=2\lbrack(1.1)^n+2(1.08)^n+4\rbrack$