Question

A club began with 3 members. Each month, each member brought one new member. Which function can be used to determine the number of members x months after the club began

Answer 1

The needed function which represents the club members after x months is :
`C(x) = 3+ (3)^x`

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 ,
`C(1) = 3 + (3)^1`

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

`\implies C(2) = 12 = 3 + (3)^2`

Continuing the same way, we can see that:

The number of members in club after x months is:

`C(x) = 3+ (3)^x`

Hence, the needed function is :
`C(x) = 3+ (3)^x`