Respuesta :
The needed function which represents the club members after x months is : [tex]C(x) = 3+ (3)^x[/tex]
Step-by-step explanation:
The initial members in the club = 3
⇒ a = 3
Also, let us assume the needed function is denoted by C(x).
Now, each member brings one new member in the club in 1 month.
So, the number of members in club after 1 month
= Initial members + Addition of members
= 3 + 3 = 6
or , [tex]C(1) = 3 + (3)^1[/tex]
Now, at the starting of second month, initial members = 6
Each member brings 1 new member.
So, the number of new members at the end of second month = 6
Total members at the end of second month = 6+ 6 = 12
[tex]\implies C(2) = 12 = 3 + (3)^2[/tex]
Continuing the same way, we can see that:
The number of members in club after x months is:
[tex]C(x) = 3+ (3)^x[/tex]
Hence, the needed function is : [tex]C(x) = 3+ (3)^x[/tex]
